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br-j16
A study of the distribution of WTV antigen within the pseudophloem cells indicates that it is irregularly distributed in the cytoplasm .
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br-j16
Wound tumor virus is a leafhopper transmitted virus not easily transmissible by mechanical inoculation (Black , 1944; Brakke et al. , 1954).
<NONE>
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br-j16
The concentration and apparent localization of the WTV antigen in pseudophloem tissue of the tumor may indicate that the virus preferentially multiplies in the phloem and may need to be directly placed in this tissue in order to infect plants .
<NONE>
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br-j17
Since emotional reactions in the higher vertebrates depend on individual experience and are aroused in man , in addition , by complex symbols , one would expect that the hypothalamus could be excited from the cortex .
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br-j17
In experiments with topical application of strychnine on the cerebral cortex , the transmission of impulses from the cortex to the hypothalamus was demonstrated .
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br-j17
Moreover , the responsiveness of the hypothalamus to nociceptive stimulation is greatly increased under these conditions .
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br-j17
Even more complex and obviously cortically induced forms of emotional arousal could be elicited in monkey A on seeing monkey B (but not a rabbit) in emotional stress .
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br-j17
A previously extinguished conditioned reaction was restored in monkey A and was associated with typical signs of emotional excitement including sympathetic discharges .
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br-j17
It seems to follow that by and large an antagonism exists between the paleo - and the neocortex as far as emotional reactivity is concerned , and that the balance between the two systems determines the emotional responsiveness of the organism .
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br-j17
In addition , the neocortical hypothalamic relations play a great role in primates , as Mirsky 's interesting experiment on the `` communication of affect '' demonstrates .
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br-j17
But even in relatively primitive laboratory animals such as the rat , sex activity closely identified with the hypothalamus and the visceral brain is enhanced by the neocortex .
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br-j17
MacLean stressed correctly the importance of the visceral brain for preservation of the individual and the species , as evidenced by the influence of the limbic brain (including the hypothalamus) on emotions related to fight and flight and also on sexual functions .
<NONE>
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br-j17
It should be added that in man neocortical hypothalamic interrelations probably play a role in the fusion of emotional processes with those underlying perception , memory , imagination , and creativity .
<NONE>
<NONE>
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br-j17
Previous experiences are obviously of great importance for the qualitative and quantitative emotional response .
<NONE>
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br-j17
The visceral brain as well as the neocortex is known to contribute to memory , but this topic is beyond the scope of this paper .
<NONE>
<NONE>
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br-j17
After this brief discussion of neo - , paleocortical , and cortico-hypothalamic relations , let us return once more to the problem of hypothalamic balance and its physiological and pathological significance .
<NONE>
<NONE>
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br-j17
Facilitatory processes take place between neocortex and hypothalamus via ascending and descending pathways .
<NONE>
<NONE>
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br-j17
Thus cortico-fugal discharges induced by topical application of strychnine to a minute area in the neocortex summate with spikes present in the hypothalamus and cause increased convulsive discharges .
<NONE>
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br-j17
On the other hand , the temporary reduction in hypothalamic excitability through the injection of a barbiturate into the posterior hypothalamus causes a lessening in frequency and amplitude of cortical strychnine spikes until the hypothalamic excitability is restored .
<NONE>
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br-j17
Apparently , a positive feedback exists between the posterior hypothalamus and the cerebral cortex .
<NONE>
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br-j17
Consequently , if for any reason the hypothalamic excitability falls below the physiological level , the lessened hypothalamic cortical discharges lead to a diminished state of activity in the cortex with consequent reduction in the cortico-fugal discharges .
<NONE>
<NONE>
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br-j17
Obviously , a vicious cycle develops .
<NONE>
<NONE>
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br-j17
This tendency can be broken either by restoring hypothalamic excitability directly or via cortico-hypothalamic pathways .
<NONE>
<NONE>
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br-j17
It is believed that drug therapy and electroshock involve the former and psychotherapy the latter mechanism .
<NONE>
<NONE>
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br-j17
Before we comment further on these pathological conditions , we should remember that changes in the state of the hypothalamus within physiological limits distinguish sleep from wakefulness .
<NONE>
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br-j17
Thus , a low intensity of hypothalamic cortical discharges prevails in sleep and a high one during wakefulness , resulting in synchronous EEG potentials in the former and asynchrony in the latter condition .
<NONE>
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br-j17
Moreover , the dominance in parasympathetic action (with reciprocal inhibition of the sympathetic) at the hypothalamic level induces , by its peripheral action , the autonomic symptoms of sleep and , by its action on the cortex , a lessening in the reactivity of the sensory and motor apparatus of the somatic nervous system .
<NONE>
<NONE>
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br-j17
With the dominance of the sympathetic division of the hypothalamus , the opposite changes occur .
<NONE>
<NONE>
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br-j17
Since electrical stimulation of the posterior hypothalamus produces the effects of wakefulness while stimulation of the anterior hypothalamus induces sleep , it may be said that the reactivity of the whole organism is altered by a change in the autonomic reactivity of the hypothalamus .
<NONE>
<NONE>
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br-j17
Similar effects can be induced reflexly via the baroreceptor reflexes in man and animals .
<NONE>
<NONE>
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br-j17
Of particular importance is the study of the actions of drugs in this respect .
<NONE>
<NONE>
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br-j17
Although no drugs act exclusively on the hypothalamus or a part of it , there is sufficient specificity to distinguish drugs which shift the hypothalamic balance to the sympathetic side from those which produce a parasympathetic dominance .
<NONE>
<NONE>
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br-j17
The former comprise analeptic and psychoactive drugs , the latter the tranquilizers .
<NONE>
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br-j17
Specific differences exist in the action of different drugs belonging to the same group as , for instance , between reserpine and chlorpromazine .
<NONE>
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br-j17
Important as these differences are , they should not obscure the basic fact that by shifting the hypothalamic balance sufficiently to the parasympathetic side , we produce depressions , whereas a shift in the opposite direction causes excitatory effects and , eventually , maniclike changes .
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br-j17
The emotional states produced by drugs influence the cortical potentials in a characteristic manner; synchrony prevails in the EEG of the experimental animal after administration of tranquilizers , but asynchrony after application of analeptic and psychoactive drugs .
<NONE>
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br-j17
The shock therapies act likewise on the hypothalamic balance .
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br-j17
Physiological experiments and clinical observations have shown that these procedures influence the hypothalamically controlled hypophyseal secretions and increase sympathetic discharges .
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br-j17
They shift the hypothalamic balance to the sympathetic side .
<NONE>
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br-j17
This explains the beneficial effect of electroshock therapy in certain depressions and a shift in the reaction from hypo - to normal reactivity of the sympathetic system as shown by the Mecholyl test .
<NONE>
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br-j17
Some investigators have found a parallelism between remissions and return of the sympathetic reactivity of the hypothalamus to the normal level as indicated by the Mecholyl test and , conversely , between clinical impairment and increasing deviation of this test from the norm .
<NONE>
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br-j17
Nevertheless , the theory that the determining influence of the hypothalamic balance has a profound influence on the clinical behavior of neuropsychiatric patients has not yet been tested on an adequate number of patients .
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br-j17
The Mecholyl and noradrenalin tests applied with certain precautions are reliable indicators of this central autonomic balance , but for the sake of correlating autonomic and clinical states , and of studying the effect of certain therapeutic procedures on central autonomic reactions , additional tests seem to be desirable .
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br-j17
It was assumed that the shift in autonomic hypothalamic balance occurring spontaneously in neuropsychiatric patients from the application of certain therapeutic procedures follows the pattern known from the sleep wakefulness cycle .
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br-j17
A change in the balance to the parasympathetic side leads in the normal individual to sleep or , in special circumstances , to cardiovascular collapse or nausea and vomiting .
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br-j17
In both conditions the emotional and perceptual sensitivity is diminished , but no depression occurs such as is seen clinically or may be produced in normal persons by drugs .
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br-j17
The fundamental differences between physiological and pathological states of parasympathetic (and also of sympathetic) dominance remain to be elucidated .
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br-j17
Perhaps a clue to these and related problems lies in the fact that changes in the intensity of hypothalamic discharges which are associated with changes in its balance lead also to qualitative alterations in reactivity .
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br-j17
A state of parasympathetic `` tuning '' of the hypothalamus induced experimentally causes not only an increase in the parasympathetic reactivity this structure to direct and reflexly induced stimuli , but leads also to an autonomic reversal: a stimulus acting sympathetically under control conditions elicits in this state of tuning a parasympathetic response !
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br-j17
Furthermore , conditioned reactions are fundamentally altered when the hypothalamic sympathetic reactivity is augmented beyond a critical level , and several types of behavioral changes probably related to the degree of central autonomic `` tuning '' are observed .
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br-j17
If , for instance , such a change is produced by one or a few insulin comas or electroshocks , previously inhibited conditioned reactions reappear .
<NONE>
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br-j17
However , if these procedures are applied more often , conditioned emotional responses are temporarily abolished .
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br-j17
In other studies , loss of differentiation in previously established conditioned reflexes resulted from repeated convulsive (metrazol) treatments , suggesting a fundamental disturbance in the balance between excitatory and inhibitory cerebral processes .
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br-j17
It has further been shown that: (1) an experimental neurosis in its initial stages is associated with a reversible shift in the central autonomic balance; (2) drugs altering the hypothalamic balance alter conditioned reactions; (3) in a state of depression , the positive conditioned stimulus may fail to elicit a conditioned reaction but cause an increased synchrony instead of the excitatory desynchronizing (alerting) effect on the EEG .
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br-j17
These are few and seemingly disjointed data , but they illustrate the important fact that fundamental alterations in conditioned reactions occur in a variety of states in which the hypothalamic balance has been altered by physiological experimentation , pharmacological action , or clinical processes .
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br-j17
The foregoing remarks imply that the hypothalamic balance plays a crucial role at the crossroads between physiological and pathological forms of emotion .
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br-j17
If this is the case , one would expect that not only the various procedures just mentioned which alter the hypothalamic balance would influence emotional state and behavior but that emotion itself would act likewise .
<NONE>
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br-j17
null
<NONE>
<NONE>
[]
[]
[]
[]
[]
[]
[]
br-j17
This phenomenon raises the question whether the guidance of the emotions for therapeutic ends may not have an even wider application in the area of the neuroses .
<NONE>
<NONE>
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br-j17
Being a strictly physiological procedure , one may expect from such a study additional information on the nature of the emotional process itself .
<NONE>
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br-j17
Wolpe 's experiments and therapeutic work lie in this area .
<NONE>
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br-j17
He showed convincingly that anxiety is a learned (conditioned) reaction and is the basis of experimental and clinical neuroses and assumed , therefore , that the neuronal changes which underlie the neuroses are functional and reversible .
<NONE>
<NONE>
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br-j17
An important observation of Pavlov served as a guide post to achieve such a reversibility by physiological means .
<NONE>
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br-j17
In a conditioning experiment , he demonstrated the antagonism between feeding and pain .
<NONE>
<NONE>
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br-j17
A mild electrical shock served as a conditioned stimulus and was followed by feeding .
<NONE>
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br-j17
The pain became thus the symbol for food and elicited salivary secretion (conditioned reflex).
<NONE>
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br-j17
Even when the intensity of the shocks was increased gradually , it failed to evoke any signs of pain .
<NONE>
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br-j17
Since strong nociceptive stimuli produce an experimental neurosis during which the animals fail to eat in the experimental situation , Wolpe thought that he could utilize the feeding pain antagonism to inhibit the neurotic symptoms through feeding .
<NONE>
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br-j17
Appropriate experiments showed that this is , indeed , possible .
<NONE>
<NONE>
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br-j17
He then applied this principle of reciprocal inhibition to human neuroses .
<NONE>
<NONE>
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br-j17
He took advantage of the antagonism between aggressive assertiveness and anxiety and found a relatively rapid disappearance of anxiety when the former attitude was established .
<NONE>
<NONE>
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br-j17
For the interpretation of these significant investigations , it should be remembered that reciprocal relations exist in the hypothalamus with respect to autonomic and somatic functions which are closely associated with the emotions .
<NONE>
<NONE>
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br-j17
The feeding pain antagonism seems to be based on this reciprocal relation between the tropho - and ergotropic systems .
<NONE>
<NONE>
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br-j17
Furthermore , a functional antagonism exists between an aggressive attitude and a state of anxiety .
<NONE>
<NONE>
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br-j17
Although in both emotions sympathetic symptoms are present , different autonomic somatic patterns underlie aggression and anxiety , respectively , as indicated by the rate of the excretion of the catecholamines , the state of the muscle tone , and the Mecholyl test .
<NONE>
<NONE>
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br-j17
The psychological incompatibility of these emotional states seems to be reflected in , or based on , this marked difference .
<NONE>
<NONE>
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br-j17
In our attempt to interpret the emotions in their physiological and pathological range , we emphasized the importance of the degree of activity of the parasympathetic and sympathetic divisions of the hypothalamic system and their influence on the inhibitory and excitatory systems , respectively .
<NONE>
<NONE>
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br-j17
We stressed the reciprocal relation of these systems with respect to the autonomic somatic downward discharge as well as regarding the hypothalamic cortical discharge .
<NONE>
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br-j17
Although we are still far from a complete understanding of these problems , as a first approximation , it is suggested that alterations in the hypothalamic balance with consequent changes in the hypothalamic cortical discharges account for major changes in behavior seen in various moods and states of emotions in man and beast under physiological circumstances , in experimental and clinical neurosis , and as the result of psychopharmacological agents .
<NONE>
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j17
In view of the important role which emotional disturbances play in the genesis of neurotic and psychotic disorders and the parallelism observed between autonomic states and psychological behavior in several instances , it is further suggested that a hypothalamic imbalance may play an important role in initiating mental changes .
<NONE>
<NONE>
[ "Compte", "tenu", "du", "rôle", "important", "que", "jouent", "les", "troubles", "émotionnels", "dans", "la", "genèse", "des", "troubles", "neurotiques", "et", "psychotiques", "et", "du", "parallélisme", "observé", "entre", "les", "états", "autonomes", "et", "le...
[ "<NONE>", "<NONE>", "<NONE>", "role%1:04:00::", "important%3:00:00::", "<NONE>", "<NONE>", "<NONE>", "emotional_disturbance%1:26:00::", "emotional_disturbance%1:26:00::", "<NONE>", "<NONE>", "genesis%1:11:00::", "<NONE>", "<NONE>", "disorder%1:26:03::", "<NONE>", "psychotic%3:00:00...
[ "<NONE>", "<NONE>", "<NONE>", "role%1:04:00", "important%3:00:00", "<NONE>", "<NONE>", "<NONE>", "emotional_disturbance%1:26:00", "emotional_disturbance%1:26:00", "<NONE>", "<NONE>", "genesis%1:11:00", "<NONE>", "<NONE>", "disorder%1:26:03", "<NONE>", "psychotic%3:00:00:insane:00",...
[ "<NONE>", "<NONE>", "3", "5", "4", "<NONE>", "6", "<NONE>", "8", "7", "<NONE>", "10", "12", "13", "<NONE>", "17", "15", "16", "18", "<NONE>", "20", "21", "<NONE>", "22", "<NONE>", "23", "25", "<NONE>", "27", "26", "28", "29", "30", "31", "<NONE>", ...
[ "<NONE>", "<NONE>", "0.113", "0.145", "0.163", "<NONE>", "0.132", "<NONE>", "0.200", "0.255", "<NONE>", "0.168", "0.221", "0.124", "<NONE>", "0.223", "0.227", "0.23", "0.184", "<NONE>", "0.257", "0.256", "<NONE>", "0.182", "<NONE>", "0.251", "0.201", "<NONE>", ...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j18
We are trying to study a linear operator T on the finite dimensional space V , by decomposing T into a direct sum of operators which are in some sense elementary .
<NONE>
<NONE>
[ "Nous", "essayons", "d&apos;", "étudier", "un", "opérateur", "linéaire", "T", "sur", "l&apos;", "espace", "dimensionnel", "fini", "V", ",", "en", "décomposant", "T", "en", "une", "somme", "directe", "d&apos;", "opérateurs", "qui", "sont", ",", "dans", "un", ...
[ "<NONE>", "try%2:41:00::", "<NONE>", "<NONE>", "study%2:31:02::", "linear_operator%1:24:00::", "linear_operator%1:24:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "dimensional%3:00:00:multidimensional:00", "finite%3:00:00::", "<NONE>", "<NONE>", "<NONE>", "decompose%2:30:00::", "<...
[ "<NONE>", "try%2:41:00", "<NONE>", "<NONE>", "study%2:31:02", "linear_operator%1:24:00", "linear_operator%1:24:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "dimensional%3:00:00:multidimensional:00", "finite%3:00:00", "<NONE>", "<NONE>", "<NONE>", "decompose%2:30:00", "<NONE>", "<...
[ "<NONE>", "2", "<NONE>", "<NONE>", "4", "7", "6", "8", "<NONE>", "9", "13", "12", "11", "14", "<NONE>", "16", "17", "18", "19", "<NONE>", "22", "21", "<NONE>", "24", "<NONE>", "26", "<NONE>", "<NONE>", "<NONE>", "28", "29", "<NONE>", "30", "<NONE>" ]
[ "<NONE>", "0.252", "<NONE>", "<NONE>", "0.253", "0.228", "0.230", "0.294", "<NONE>", "0.208", "0.227", "0.263", "0.184", "0.304", "<NONE>", "0.307", "0.344", "0.287", "0.195", "<NONE>", "0.194", "0.199", "<NONE>", "0.318", "<NONE>", "0.217", "<NONE>", "<NONE>", ...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j18
We can do this through the characteristic values and vectors of T in certain special cases , i.e. , when the minimal polynomial for T factors over the scalar field F into a product of distinct monic polynomials of degree 1 .
<NONE>
<NONE>
[ "Nous", "pouvons", "le", "faire", "par", "le", "biais", "des", "valeurs", "et", "vecteurs", "caractéristiques", "de", "T", "dans", "certains", "cas", "spéciaux", ",", "c&apos;", "est", "@-@", "à", "@-@", "dire", "lorsque", "le", "polynôme", "minimal", "pour"...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "value%1:09:00::", "characteristic%3:00:00::", "vector%1:09:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "certain%3:00:00:definite:00", "<NONE>", "special%3:00:01:specific:00", "<NONE>", "i.e.%4:0...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "value%1:09:00", "characteristic%3:00:00", "vector%1:09:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "certain%3:00:00:definite:00", "<NONE>", "special%3:00:01:specific:00", "<NONE>", "i.e.%4:02:00",...
[ "<NONE>", "<NONE>", "1", "3", "<NONE>", "4", "<NONE>", "<NONE>", "7", "6", "9", "<NONE>", "10", "11", "<NONE>", "13", "<NONE>", "14", "<NONE>", "17", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "19", "<NONE>", "22", "21", "<NONE>", "23", "<NONE>", ...
[ "<NONE>", "<NONE>", "0.182", "0.199", "<NONE>", "0.206", "<NONE>", "<NONE>", "0.158", "0.199", "0.222", "<NONE>", "0.152", "0.201", "<NONE>", "0.203", "<NONE>", "0.236", "<NONE>", "0.216", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "0.277", "<NONE>", "0.2...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j18
What can we do with the general T ?
<NONE>
<NONE>
[ "Que", "pouvons", "@-@", "nous", "faire", "avec", "le", "T", "général", "?" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "do%2:41:01::", "<NONE>", "<NONE>", "<NONE>", "general%3:00:00::", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "do%2:41:01", "<NONE>", "<NONE>", "<NONE>", "general%3:00:00", "<NONE>" ]
[ "<NONE>", "1", "2", "<NONE>", "3", "4", "7", "<NONE>", "6", "8" ]
[ "<NONE>", "0.260", "0.249", "<NONE>", "0.298", "0.301", "0.259", "<NONE>", "0.362", "0.265" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j18
If we try to study T using characteristic values , we are confronted with two problems .
<NONE>
<NONE>
[ "Si", "nous", "essayons", "d&apos;", "étudier", "T", "en", "utilisant", "des", "valeurs", "caractéristiques", ",", "nous", "sommes", "confrontés", "à", "deux", "problèmes", "." ]
[ "<NONE>", "<NONE>", "try%2:41:00::", "<NONE>", "study%2:31:02::", "<NONE>", "<NONE>", "use%2:34:01::", "<NONE>", "value%1:09:00::", "characteristic%3:00:00::", "<NONE>", "<NONE>", "<NONE>", "confront%2:32:03::", "<NONE>", "two%3:00:00:cardinal:00", "problem%1:10:00::", "<NONE>" ]
[ "<NONE>", "<NONE>", "try%2:41:00", "<NONE>", "study%2:31:02", "<NONE>", "<NONE>", "use%2:34:01", "<NONE>", "value%1:09:00", "characteristic%3:00:00", "<NONE>", "<NONE>", "<NONE>", "confront%2:32:03", "<NONE>", "two%3:00:00:cardinal:00", "problem%1:10:00", "<NONE>" ]
[ "<NONE>", "1", "2", "<NONE>", "4", "5", "<NONE>", "6", "<NONE>", "8", "7", "<NONE>", "<NONE>", "10", "12", "<NONE>", "14", "15", "<NONE>" ]
[ "<NONE>", "0.206", "0.323", "<NONE>", "0.289", "0.380", "<NONE>", "0.343", "<NONE>", "0.343", "0.397", "<NONE>", "<NONE>", "0.199", "0.337", "<NONE>", "0.300", "0.323", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j18
First , T may not have a single characteristic value; this is really a deficiency in the scalar field , namely , that it is not algebraically closed .
<NONE>
<NONE>
[ "Premièrement", ",", "T", "n&apos;", "a", "peut", "@-@", "être", "pas", "une", "seule", "valeur", "caractéristique", ";", "il", "s&apos;", "agit", "en", "fait", "d&apos;", "une", "lacune", "dans", "le", "domaine", "scalaire", ",", "à", "savoir", "qu&apos;", ...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "not%4:02:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "single%3:00:00::", "<NONE>", "characteristic%3:00:00::", "value%1:09:00::", "<NONE>", "<NONE>", "be%2:42:06::", "<NONE>", "really%4:02:03::", "<NONE>", "<NONE>", "def...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "not%4:02:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "single%3:00:00", "<NONE>", "characteristic%3:00:00", "value%1:09:00", "<NONE>", "<NONE>", "be%2:42:06", "<NONE>", "really%4:02:03", "<NONE>", "<NONE>", "deficiency%1:26...
[ "<NONE>", "<NONE>", "<NONE>", "2", "4", "3", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "7", "<NONE>", "8", "9", "<NONE>", "10", "11", "<NONE>", "12", "<NONE>", "<NONE>", "14", "<NONE>", "15", "18", "17", "<NONE>", "20", "<NONE>", "<NONE>", "22", "<NONE>", ...
[ "<NONE>", "<NONE>", "<NONE>", "0.225", "0.187", "0.186", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "0.229", "<NONE>", "0.308", "0.191", "<NONE>", "0.135", "0.155", "<NONE>", "0.354", "<NONE>", "<NONE>", "0.329", "<NONE>", "0.180", "0.231", "0.266", "<NONE>", "0.26...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j18
Second , even if the characteristic polynomial factors completely over F into a product of polynomials of degree 1 , there may not be enough characteristic vectors for T to span the space V; this is clearly a deficiency in T .
<NONE>
<NONE>
[ "Deuxièmement", ",", "même", "si", "les", "facteurs", "polynomiaux", "caractéristiques", "complètement", "au", "@-@", "dessus", "de", "F", "dans", "un", "produit", "de", "polynômes", "du", "degré", "1", ",", "il", "n&apos;", "y", "a", "peut", "@-@", "être", ...
[ "<NONE>", "<NONE>", "even%4:02:00::", "<NONE>", "<NONE>", "factor%2:31:00::", "polynomial%1:09:00::", "characteristic%3:00:00::", "completely%4:02:03::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "product%1:09:00::", "<NONE>", "polynomial%1:09:00::", ...
[ "<NONE>", "<NONE>", "even%4:02:00", "<NONE>", "<NONE>", "factor%2:31:00", "polynomial%1:09:00", "characteristic%3:00:00", "completely%4:02:03", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "product%1:09:00", "<NONE>", "polynomial%1:09:00", "<NONE>", "...
[ "<NONE>", "<NONE>", "2", "3", "4", "7", "6", "5", "8", "<NONE>", "9", "<NONE>", "<NONE>", "10", "<NONE>", "11", "13", "<NONE>", "15", "<NONE>", "17", "18", "<NONE>", "20", "21", "22", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "24", "<NONE>", ...
[ "<NONE>", "<NONE>", "0.189", "0.258", "0.124", "0.155", "0.288", "0.228", "0.192", "<NONE>", "0.286", "<NONE>", "<NONE>", "0.229", "<NONE>", "0.174", "0.249", "<NONE>", "0.273", "<NONE>", "0.318", "0.257", "<NONE>", "0.140", "0.245", "0.119", "<NONE>", "<NONE>",...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j18
The second situation is illustrated by the operator T on * * f (F any field) represented in the standard basis by * * f .
<NONE>
<NONE>
[ "Le", "deuxième", "cas", "de", "figure", "est", "illustré", "par", "l&apos;", "opérateur", "T", "sur", "*", "*", "f", ",", "le", "cas", "échéant", ")", "représenté", "dans", "la", "base", "standard", "par", "*", "*", "f." ]
[ "<NONE>", "second%3:00:00::", "situation%1:26:00::", "<NONE>", "<NONE>", "<NONE>", "illustrate%2:32:00::", "<NONE>", "<NONE>", "operator%1:24:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "represent%2:42...
[ "<NONE>", "second%3:00:00", "situation%1:26:00", "<NONE>", "<NONE>", "<NONE>", "illustrate%2:32:00", "<NONE>", "<NONE>", "operator%1:24:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "represent%2:42:02", ...
[ "<NONE>", "1", "2", "<NONE>", "<NONE>", "3", "4", "5", "<NONE>", "7", "8", "9", "<NONE>", "11", "12", "13", "<NONE>", "<NONE>", "<NONE>", "14", "<NONE>", "16", "17", "<NONE>", "20", "21", "22", "23", "24" ]
[ "<NONE>", "0.177", "0.257", "<NONE>", "<NONE>", "0.154", "0.268", "0.229", "<NONE>", "0.322", "0.266", "0.204", "<NONE>", "0.218", "0.271", "0.478", "<NONE>", "<NONE>", "<NONE>", "0.180", "<NONE>", "0.265", "0.190", "<NONE>", "0.323", "0.203", "0.230", "0.247", ...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
br-j18
The characteristic polynomial for A is * * f and this is plainly also the minimal polynomial for A (or for T).
<NONE>
<NONE>
[ "Le", "polynôme", "caractéristique", "de", "A", "est", "*", "*", "f", "et", "il", "s&apos;", "agit", "manifestement", "aussi", "du", "polynôme", "minimal", "de", "A", "et", "de", "Ti", "." ]
[ "<NONE>", "polynomial%1:09:00::", "characteristic%3:00:00::", "<NONE>", "<NONE>", "be%2:42:06::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "plainly%4:02:00::", "also%4:02:00::", "<NONE>", "polynomial%1:09:00::", "minimal%3:00:00::", "<NONE>", "<NONE...
[ "<NONE>", "polynomial%1:09:00", "characteristic%3:00:00", "<NONE>", "<NONE>", "be%2:42:06", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "plainly%4:02:00", "also%4:02:00", "<NONE>", "polynomial%1:09:00", "minimal%3:00:00", "<NONE>", "<NONE>", "<NONE>"...
[ "<NONE>", "2", "1", "<NONE>", "4", "5", "6", "7", "8", "<NONE>", "9", "<NONE>", "10", "12", "13", "14", "16", "15", "<NONE>", "<NONE>", "19", "<NONE>", "21", "<NONE>" ]
[ "<NONE>", "0.270", "0.329", "<NONE>", "0.201", "0.230", "0.215", "0.299", "0.298", "<NONE>", "0.160", "<NONE>", "0.160", "0.217", "0.232", "0.175", "0.268", "0.263", "<NONE>", "<NONE>", "0.543", "<NONE>", "0.548", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j18
Thus T is not diagonalizable .
<NONE>
<NONE>
[ "Ainsi", ",", "T", "n&apos;", "est", "pas", "diagonalisable", "." ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "be%2:42:03::", "not%4:02:00::", "diagonalizable%3:01:00::", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "be%2:42:03", "not%4:02:00", "diagonalizable%3:01:00", "<NONE>" ]
[ "<NONE>", "<NONE>", "1", "<NONE>", "2", "3", "4", "<NONE>" ]
[ "<NONE>", "<NONE>", "0.348", "<NONE>", "0.316", "0.238", "0.473", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j18
One sees that this happens because the null space of * * f has dimension 1 only .
<NONE>
<NONE>
[ "On", "voit", "que", "cela", "se", "produit", "parce", "que", "l&apos;", "espace", "nul", "de", "*", "*", "f", "n&apos;", "a", "que", "la", "dimension", "1", "." ]
[ "<NONE>", "see%2:31:01::", "<NONE>", "<NONE>", "<NONE>", "happen%2:30:02::", "<NONE>", "<NONE>", "<NONE>", "null_space%1:14:00::", "null_space%1:14:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "have%2:42:00::", "only%4:02:01::", "<NONE>", "<NONE>", "dimension%1:07:00::", "1...
[ "<NONE>", "see%2:31:01", "<NONE>", "<NONE>", "<NONE>", "happen%2:30:02", "<NONE>", "<NONE>", "<NONE>", "null_space%1:14:00", "null_space%1:14:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "have%2:42:00", "only%4:02:01", "<NONE>", "<NONE>", "dimension%1:07:00", "1%1:23:00", "...
[ "<NONE>", "1", "<NONE>", "3", "<NONE>", "4", "5", "<NONE>", "<NONE>", "8", "7", "9", "10", "11", "12", "13", "16", "<NONE>", "<NONE>", "14", "15", "<NONE>" ]
[ "<NONE>", "0.329", "<NONE>", "0.237", "<NONE>", "0.316", "0.260", "<NONE>", "<NONE>", "0.235", "0.254", "0.173", "0.230", "0.303", "0.301", "0.290", "0.269", "<NONE>", "<NONE>", "0.375", "0.266", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
br-j18
On the other hand , the null space of * * f and the null space of * * f together span V , the former being the subspace spanned by * * f and the latter the subspace spanned by * * f and * * f .
<NONE>
<NONE>
[ "Par", "contre", ",", "l&apos;", "espace", "nul", "de", "*", "*", "f", "et", "l&apos;", "espace", "nul", "de", "*", "*", "f", "ensemble", "l&apos;", "étendue", "V", ",", "le", "premier", "étant", "le", "sous", "@-@", "espace", "couvert", "par", "*", ...
[ "<NONE>", "on_the_other_hand%4:02:00::", "<NONE>", "<NONE>", "null_space%1:14:00::", "null_space%1:14:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "null_space%1:14:00::", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "span%2:42:00...
[ "<NONE>", "on_the_other_hand%4:02:00", "<NONE>", "<NONE>", "null_space%1:14:00", "null_space%1:14:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "null_space%1:14:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "span%2:42:00", "<N...
[ "<NONE>", "2", "4", "5", "7", "6", "8", "9", "10", "11", "12", "<NONE>", "<NONE>", "15", "16", "17", "18", "19", "20", "<NONE>", "21", "<NONE>", "22", "24", "25", "<NONE>", "26", "28", "<NONE>", "28", "29", "30", "31", "32", "33", "34", "35", ...
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br-j18
This will be more or less our general method for the second problem .
<NONE>
<NONE>
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br-j18
If (remember this is an assumption) the minimal polynomial for T decomposes * * f where * * f are distinct elements of F , then we shall show that the space V is the direct sum of the null spaces of * * f .
<NONE>
<NONE>
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br-j18
The diagonalizable operator is the special case of this in which * * f for each i .
<NONE>
<NONE>
[ "L&apos;", "opérateur", "diagonalisable", "est", "le", "cas", "particulier", "dans", "lequel", "*", "*", "f", "pour", "chaque", "i." ]
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br-j18
The theorem which we prove is more general than what we have described , since it works with the primary decomposition of the minimal polynomial , whether or not the primes which enter are all of first degree .
<NONE>
<NONE>
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
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br-j18
The reader will find it helpful to think of the special case when the primes are of degree 1 , and even more particularly , to think of the proof of Theorem 10 , a special case of this theorem .
<NONE>
<NONE>
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[ "<NONE>", "reader%1:18:00::", "<NONE>", "helpful%3:00:00::", "<NONE>", "think_of%2:31:00::", "<NONE>", "<NONE>", "case%1:11:00::", "<NONE>", "<NONE>", "prime%1:23:00::", "<NONE>", "<NONE>", "degree%1:09:00::", "<NONE>", "1%1:23:00::", "<NONE>", "even%4:02:00::", "more%3:00:01::...
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NO...
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br-j18
Let T be a linear operator on the finite dimensional vector space V over the field F .
<NONE>
<NONE>
[ "Soit", "T", "un", "opérateur", "linéaire", "sur", "l&apos;", "espace", "vectoriel", "fini", "V", "sur", "le", "champ", "F." ]
[ "<NONE>", "<NONE>", "<NONE>", "linear_operator%1:24:00::", "linear_operator%1:24:00::", "<NONE>", "<NONE>", "<NONE>", "vector%1:09:00::", "dimensional%3:01:00::", "<NONE>", "<NONE>", "<NONE>", "field%1:14:00::", "<NONE>" ]
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br-j18
Let p be the minimal polynomial for T , * * f where the * * f are distinct irreducible monic polynomials over F and the * * f are positive integers .
<NONE>
<NONE>
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br-j18
Let * * f be the null space of * * f .
<NONE>
<NONE>
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[ "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "<NONE>", "null_space%1:14:00", "<NONE>", "<NONE>", "<NONE>", "<NONE>" ]
[ "<NONE>", "<NONE>", "2", "3", "<NONE>", "<NONE>", "7", "8", "9", "10", "11" ]
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br-j18
Then (a) * * f (b) each * * f is invariant under T (c) if * * f is the operator induced on * * f by T , then the minimal polynomial for * * f is * * f .
<NONE>
<NONE>
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