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First degree equation Summary Linear_constraint Often, the term linear equation refers implicitly to this particular case, in which the variable is sensibly called the unknown. In the case of two variables, each solution may be interpreted as the Cartesian coordinates of a point of the Euclidean plane. The solutions of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
First degree equation Summary Linear_constraint This is the origin of the term linear for describing this type of equations. More generally, the solutions of a linear equation in n variables form a hyperplane (a subspace of dimension n − 1) in the Euclidean space of dimension n. Linear equations occur frequently in all... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dual vector Summary Dual_vector In mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear map from a vector space to its field of scalars (often, the real numbers or the complex numbers). If V is a vector space over a field k, the set of all linear functionals from V to k ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Dual vector Summary Dual_vector It is often denoted Hom(V, k), or, when the field k is understood, V ∗ {\displaystyle V^{*}} ; other notations are also used, such as V ′ {\displaystyle V'} , V # {\displaystyle V^{\#}} or V ∨ . {\displaystyle V^{\vee }.} When vectors are represented by column vectors (as is common when ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Linear fractional transformations Summary Linear_fractional_transformation In mathematics, a linear fractional transformation is, roughly speaking, an invertible transformation of the form z ↦ a z + b c z + d . {\displaystyle z\mapsto {\frac {az+b}{cz+d}}.} The precise definition depends on the nature of a, b, c, d, an... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Linear fractional transformations Summary Linear_fractional_transformation The invertibility condition is then ad – bc ≠ 0. Over a field, a linear fractional transformation is the restriction to the field of a projective transformation or homography of the projective line. When a, b, c, d are integer (or, more generall... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Linear fractional transformations Summary Linear_fractional_transformation In this case, the invertibility condition is that ad – bc must be a unit of the domain (that is 1 or −1 in the case of integers).In the most general setting, the a, b, c, d and z are elements of a ring, such as square matrices. An example of suc... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nonlinear science Definition Non-linear_differential_equation > Definition In mathematics, a linear map (or linear function) f ( x ) {\displaystyle f(x)} is one which satisfies both of the following properties: Additivity or superposition principle: f ( x + y ) = f ( x ) + f ( y ) ; {\displaystyle \textstyle f(x+y)=f(x... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nonlinear science Definition Non-linear_differential_equation > Definition The conditions of additivity and homogeneity are often combined in the superposition principle f ( α x + β y ) = α f ( x ) + β f ( y ) {\displaystyle f(\alpha x+\beta y)=\alpha f(x)+\beta f(y)} An equation written as f ( x ) = C {\displaystyle f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Linearity Linear maps Linearity > In mathematics > Linear maps In mathematics, a linear map or linear function f(x) is a function that satisfies the two properties: Additivity: f(x + y) = f(x) + f(y). Homogeneity of degree 1: f(αx) = α f(x) for all α.These properties are known as the superposition principle. In this de... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Linearity Linear maps Linearity > In mathematics > Linear maps Additivity alone implies homogeneity for rational α, since f ( x + x ) = f ( x ) + f ( x ) {\displaystyle f(x+x)=f(x)+f(x)} implies f ( n x ) = n f ( x ) {\displaystyle f(nx)=nf(x)} for any natural number n by mathematical induction, and then n f ( x ) = f ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Semi-simple operator Summary Semi-simple_operator In mathematics, a linear operator T on a vector space is semisimple if every T-invariant subspace has a complementary T-invariant subspace; in other words, the vector space is a semisimple representation of the operator T. Equivalently, a linear operator is semisimple i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Locally finite operator Summary Locally_finite_operator In mathematics, a linear operator f: V → V {\displaystyle f:V\to V} is called locally finite if the space V {\displaystyle V} is the union of a family of finite-dimensional f {\displaystyle f} -invariant subspaces. : 40 In other words, there exists a family { V i ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Linearized polynomial Summary Linearised_polynomial In mathematics, a linearised polynomial (or q-polynomial) is a polynomial for which the exponents of all the constituent monomials are powers of q and the coefficients come from some extension field of the finite field of order q. We write a typical example as where e... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Linked field Summary Linked_field In mathematics, a linked field is a field for which the quadratic forms attached to quaternion algebras have a common property. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Local language (formal language) Summary Local_language_(formal_language) In mathematics, a local language is a formal language for which membership of a word in the language can be determined by looking at the first and last symbol and each two-symbol substring of the word. Equivalently, it is a language recognised by... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Local martingale Summary Local_martingale In mathematics, a local martingale is a type of stochastic process, satisfying the localized version of the martingale property. Every martingale is a local martingale; every bounded local martingale is a martingale; in particular, every local martingale that is bounded from be... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Local coefficients Summary Local_coefficients In mathematics, a local system (or a system of local coefficients) on a topological space X is a tool from algebraic topology which interpolates between cohomology with coefficients in a fixed abelian group A, and general sheaf cohomology in which coefficients vary from poi... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Locally catenative sequence Summary Locally_catenative_sequence In mathematics, a locally catenative sequence is a sequence of words in which each word can be constructed as the concatenation of previous words in the sequence.Formally, an infinite sequence of words w(n) is locally catenative if, for some positive integ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Locally compact group Summary Locally_compact_group In mathematics, a locally compact group is a topological group G for which the underlying topology is locally compact and Hausdorff. Locally compact groups are important because many examples of groups that arise throughout mathematics are locally compact and such gro... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Locally compact group Summary Locally_compact_group For compact groups, modifications of these proofs yields similar results by averaging with respect to the normalized Haar integral. In the general locally compact setting, such techniques need not hold. The resulting theory is a central part of harmonic analysis. The ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Kazhdan's property (T) Summary Kazhdan's_property_(T) In mathematics, a locally compact topological group G has property (T) if the trivial representation is an isolated point in its unitary dual equipped with the Fell topology. Informally, this means that if G acts unitarily on a Hilbert space and has "almost invarian... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Locally constant function Summary Locally_constant_function In mathematics, a locally constant function is a function from a topological space into a set with the property that around every point of its domain, there exists some neighborhood of that point on which it restricts to a constant function. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Locally cyclic group Summary Locally_cyclic_group In mathematics, a locally cyclic group is a group (G, *) in which every finitely generated subgroup is cyclic. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Locally finite measure Summary Locally_finite_measure In mathematics, a locally finite measure is a measure for which every point of the measure space has a neighbourhood of finite measure. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Locally finite partially ordered set Summary Locally_finite_partially_ordered_set In mathematics, a locally finite poset is a partially ordered set P such that for all x, y ∈ P, the interval consists of finitely many elements. Given a locally finite poset P we can define its incidence algebra. Elements of the incidenc... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Locally finite partially ordered set Summary Locally_finite_partially_ordered_set {\displaystyle (f*g)(x,y):=\sum _{x\leq z\leq y}f(x,z)g(z,y).} There is also a definition of incidence coalgebra. In theoretical physics a locally finite poset is also called a causal set and has been used as a model for spacetime. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Locally integrable function Summary Locally_integrable In mathematics, a locally integrable function (sometimes also called locally summable function) is a function which is integrable (so its integral is finite) on every compact subset of its domain of definition. The importance of such functions lies in the fact that... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Locally profinite group Summary Locally_profinite_group In mathematics, a locally profinite group is a Hausdorff topological group in which every neighborhood of the identity element contains a compact open subgroup. Equivalently, a locally profinite group is a topological group that is Hausdorff, locally compact, and ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Locally simply connected space Summary Locally_simply_connected In mathematics, a locally simply connected space is a topological space that admits a basis of simply connected sets. Every locally simply connected space is also locally path-connected and locally connected. The circle is an example of a locally simply co... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Locally simply connected space Summary Locally_simply_connected The cone on the Hawaiian earring is contractible and therefore simply connected, but still not locally simply connected. All topological manifolds and CW complexes are locally simply connected. In fact, these satisfy the much stronger property of being loc... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Locally simply connected space Summary Locally_simply_connected A strictly weaker condition is that of being semi-locally simply connected. Both locally simply connected spaces and simply connected spaces are semi-locally simply connected, but neither converse holds. == References == | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Logarithm of a matrix Summary Logarithm_of_a_matrix In mathematics, a logarithm of a matrix is another matrix such that the matrix exponential of the latter matrix equals the original matrix. It is thus a generalization of the scalar logarithm and in some sense an inverse function of the matrix exponential. Not all mat... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Disjunct matrix Summary Disjunct_matrix In mathematics, a logical matrix may be described as d-disjunct and/or d-separable. These concepts play a pivotal role in the mathematical area of non-adaptive group testing. In the mathematical literature, d-disjunct matrices may also be called super-imposed codes or d-cover-fre... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Disjunct matrix Summary Disjunct_matrix A matrix is said to be d-disjunct if no set of d columns has a boolean sum which is a superset of any other single column.The following relationships are "well-known": Every d + 1 ¯ {\displaystyle {\overline {d+1}}} -separable matrix is also d {\displaystyle d} -disjunct. Every d... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Loop group Summary Loop_group In mathematics, a loop group is a group of loops in a topological group G with multiplication defined pointwise. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Loop (topology) Summary Loop_(topology) In mathematics, a loop in a topological space X is a continuous function f from the unit interval I = to X such that f(0) = f(1). In other words, it is a path whose initial point is equal to its terminal point.A loop may also be seen as a continuous map f from the pointed unit c... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Quasi-random sequence Summary Quasi-random_sequences In mathematics, a low-discrepancy sequence is a sequence with the property that for all values of N, its subsequence x1, ..., xN has a low discrepancy. Roughly speaking, the discrepancy of a sequence is low if the proportion of points in the sequence falling into an ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Magic cube Summary Magic_cube In mathematics, a magic cube is the 3-dimensional equivalent of a magic square, that is, a collection of integers arranged in an n × n × n pattern such that the sums of the numbers on each row, on each column, on each pillar and on each of the four main space diagonals are equal, the so-ca... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nasik magic hypercube Summary Magic_tesseract In mathematics, a magic hypercube is the k-dimensional generalization of magic squares and magic cubes, that is, an n × n × n × ... × n array of integers such that the sums of the numbers on each pillar (along any axis) as well as on the main space diagonals are all the sam... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nasik magic hypercube Summary Magic_tesseract Four-, five-, six-, seven- and eight-dimensional magic hypercubes of order three have been constructed by J. R. Hendricks. Marian Trenkler proved the following theorem: A p-dimensional magic hypercube of order n exists if and only if p > 1 and n is different from 2 or p = 1... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Manifold theory Summary Manifold_with_corners In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n {\displaystyle n} -dimensional manifold, or n {\displaystyle n} -manifold for short, is a topological space with the property that each point has a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Manifold theory Summary Manifold_with_corners Examples include the plane, the sphere, and the torus, and also the Klein bottle and real projective plane. The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows complicated structures to be described in terms of we... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Manifold theory Summary Manifold_with_corners The concept has applications in computer-graphics given the need to associate pictures with coordinates (e.g. CT scans). Manifolds can be equipped with additional structure. One important class of manifolds are differentiable manifolds; their differentiable structure allows... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Manifold theory Summary Manifold_with_corners A Riemannian metric on a manifold allows distances and angles to be measured. Symplectic manifolds serve as the phase spaces in the Hamiltonian formalism of classical mechanics, while four-dimensional Lorentzian manifolds model spacetime in general relativity. The study of ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Map (mathematics) Summary Map_(mathematics) In mathematics, a map or mapping is a function in its general sense. These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper.The term map may be used to distinguish some special types of functions, such a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Map (mathematics) Summary Map_(mathematics) In category theory, a map may refer to a morphism. The term transformation can be used interchangeably, but transformation often refers to a function from a set to itself. There are also a few less common uses in logic and graph theory. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
P-local subgroup Summary P-local_subgroup In mathematics, a mathematical object is said to satisfy a property locally, if the property is satisfied on some limited, immediate portions of the object (e.g., on some sufficiently small or arbitrarily small neighborhoods of points). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Principal submatrix Summary Real_matrices In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three colum... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Principal submatrix Summary Real_matrices Therefore, the study of matrices is a large part of linear algebra, and most properties and operations of abstract linear algebra can be expressed in terms of matrices. For example, matrix multiplication represents the composition of linear maps. Not all matrices are related to... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Principal submatrix Summary Real_matrices This is, in particular, the case in graph theory, of incidence matrices, and adjacency matrices. This article focuses on matrices related to linear algebra, and, unless otherwise specified, all matrices represent linear maps or may be viewed as such. Square matrices, matrices w... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Principal submatrix Summary Real_matrices Square matrices of a given dimension form a noncommutative ring, which is one of the most common examples of a noncommutative ring. The determinant of a square matrix is a number associated to the matrix, which is fundamental for the study of a square matrix; for example, a squ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Principal submatrix Summary Real_matrices In numerical analysis, many computational problems are solved by reducing them to a matrix computation, and this often involves computing with matrices of huge dimension. Matrices are used in most areas of mathematics and most scientific fields, either directly, or through thei... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Matrix coefficient Summary Representative_function In mathematics, a matrix coefficient (or matrix element) is a function on a group of a special form, which depends on a linear representation of the group and additional data. Precisely, it is a function on a compact topological group G obtained by composing a represen... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Matrix coefficient Summary Representative_function They arise naturally from finite-dimensional representations of G as the matrix-entry functions of the corresponding matrix representations. The Peter–Weyl theorem says that the matrix coefficients on G are dense in the Hilbert space of square-integrable functions on G... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Matrix factorization of a polynomial Summary Matrix_factorization_of_a_polynomial In mathematics, a matrix factorization of a polynomial is a technique for factoring irreducible polynomials with matrices. David Eisenbud proved that every multivariate real-valued polynomial p without linear terms can be written as a AB ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Matrix group Summary Linear_group In mathematics, a matrix group is a group G consisting of invertible matrices over a specified field K, with the operation of matrix multiplication. A linear group is a group that is isomorphic to a matrix group (that is, admitting a faithful, finite-dimensional representation over K).... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
M-theory BFSS matrix model M-theory > Matrix theory > BFSS matrix model In mathematics, a matrix is a rectangular array of numbers or other data. In physics, a matrix model is a particular kind of physical theory whose mathematical formulation involves the notion of a matrix in an important way. A matrix model describe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
M-theory BFSS matrix model M-theory > Matrix theory > BFSS matrix model In their original paper, these authors showed, among other things, that the low energy limit of this matrix model is described by eleven-dimensional supergravity. These calculations led them to propose that the BFSS matrix model is exactly equivale... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gauge–gravity duality Matrix theory String_theorist > M-theory > Matrix theory In mathematics, a matrix is a rectangular array of numbers or other data. In physics, a matrix model is a particular kind of physical theory whose mathematical formulation involves the notion of a matrix in an important way. A matrix model d... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gauge–gravity duality Matrix theory String_theorist > M-theory > Matrix theory In their original paper, these authors showed, among other things, that the low energy limit of this matrix model is described by eleven-dimensional supergravity. These calculations led them to propose that the BFSS matrix model is exactly e... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gauge–gravity duality Matrix theory String_theorist > M-theory > Matrix theory This subject is a generalization of ordinary geometry in which mathematicians define new geometric notions using tools from noncommutative algebra. In a paper from 1998, Alain Connes, Michael R. Douglas, and Albert Schwarz showed that some a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Conformable matrix Summary Conformable_matrix In mathematics, a matrix is conformable if its dimensions are suitable for defining some operation (e.g. addition, multiplication, etc.). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Spectral norm Summary Spectral_norm In mathematics, a matrix norm is a vector norm in a vector space whose elements (vectors) are matrices (of given dimensions). | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Matrix of ones Summary All-ones_vector In mathematics, a matrix of ones or all-ones matrix is a matrix where every entry is equal to one. Examples of standard notation are given below: J 2 = ( 1 1 1 1 ) ; J 3 = ( 1 1 1 1 1 1 1 1 1 ) ; J 2 , 5 = ( 1 1 1 1 1 1 1 1 1 1 ) ; J 1 , 2 = ( 1 1 ) . {\displaystyle J_{2}={\begin{... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Matrix geometrical series Summary Matrix_polynomial In mathematics, a matrix polynomial is a polynomial with square matrices as variables. Given an ordinary, scalar-valued polynomial P ( x ) = ∑ i = 0 n a i x i = a 0 + a 1 x + a 2 x 2 + ⋯ + a n x n , {\displaystyle P(x)=\sum _{i=0}^{n}{a_{i}x^{i}}=a_{0}+a_{1}x+a_{2}x^{... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Matroid polytope Summary Matroid_polytope In mathematics, a matroid polytope, also called a matroid basis polytope (or basis matroid polytope) to distinguish it from other polytopes derived from a matroid, is a polytope constructed via the bases of a matroid. Given a matroid M {\displaystyle M} , the matroid polytope P... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Maximal compact subgroup Summary Maximal_compact_subgroup In mathematics, a maximal compact subgroup K of a topological group G is a subgroup K that is a compact space, in the subspace topology, and maximal amongst such subgroups. Maximal compact subgroups play an important role in the classification of Lie groups and ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Meander (mathematics) Summary Open_meandric_number In mathematics, a meander or closed meander is a self-avoiding closed curve which crosses a given line a number of times, meaning that it intersects the line while passing from one side to the other. Intuitively, a meander can be viewed as a meandering river with a str... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Measurable group action Summary Measurable_acting_group In mathematics, a measurable acting group is a special group that acts on some space in a way that is compatible with structures of measure theory. Measurable acting groups are found in the intersection of measure theory and group theory, two sub-disciplines of ma... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Measurable cardinal Summary Measurable_cardinal In mathematics, a measurable cardinal is a certain kind of large cardinal number. In order to define the concept, one introduces a two-valued measure on a cardinal κ, or more generally on any set. For a cardinal κ, it can be described as a subdivision of all of its subset... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Measurable group Summary Measurable_group In mathematics, a measurable group is a special type of group in the intersection between group theory and measure theory. Measurable groups are used to study measures is an abstract setting and are often closely related to topological groups. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Measurable space Summary Measurable_space In mathematics, a measurable space or Borel space is a basic object in measure theory. It consists of a set and a σ-algebra, which defines the subsets that will be measured. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Measure algebra Summary Measure_algebra In mathematics, a measure algebra is a Boolean algebra with a countably additive positive measure. A probability measure on a measure space gives a measure algebra on the Boolean algebra of measurable sets modulo null sets. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Locally measurable set Summary Locally_measurable_set In mathematics, a measure is said to be saturated if every locally measurable set is also measurable. A set E {\displaystyle E} , not necessarily measurable, is said to be a locally measurable set if for every measurable set A {\displaystyle A} of finite measure, E ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Transverse measure Summary Transverse_measure In mathematics, a measure on a real vector space is said to be transverse to a given set if it assigns measure zero to every translate of that set, while assigning finite and positive (i.e. non-zero) measure to some compact set. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Measure preserving dynamical system Summary Metric_entropy In mathematics, a measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular. Measure-preserving systems obey the Poincaré recurrence theorem, and are a special case of conservati... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Metabelian group Summary Metabelian_group In mathematics, a metabelian group is a group whose commutator subgroup is abelian. Equivalently, a group G is metabelian if and only if there is an abelian normal subgroup A such that the quotient group G/A is abelian. Subgroups of metabelian groups are metabelian, as are imag... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Metasymplectic space Summary Metasymplectic_space In mathematics, a metasymplectic space, introduced by Freudenthal (1959) and Tits (1974, 10.13), is a Tits building of type F4 (a specific generalized incidence structure). The four types of vertices are called points, lines, planes, and symplecta. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Riemannian connection Summary Metric_compatible In mathematics, a metric connection is a connection in a vector bundle E equipped with a bundle metric; that is, a metric for which the inner product of any two vectors will remain the same when those vectors are parallel transported along any curve. This is equivalent to... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Riemannian connection Summary Metric_compatible In this case, the bundle E is the tangent bundle TM of a manifold, and the metric on E is induced by a Riemannian metric on M. Another special case of a metric connection is a Yang–Mills connection, which satisfies the Yang–Mills equations of motion. Most of the machinery... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Metric outer measure Summary Metric_outer_measure In mathematics, a metric outer measure is an outer measure μ defined on the subsets of a given metric space (X, d) such that μ ( A ∪ B ) = μ ( A ) + μ ( B ) {\displaystyle \mu (A\cup B)=\mu (A)+\mu (B)} for every pair of positively separated subsets A and B of X. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Doubling dimension Summary Doubling_dimension In mathematics, a metric space X with metric d is said to be doubling if there is some doubling constant M > 0 such that for any x ∈ X and r > 0, it is possible to cover the ball B(x, r) = {y | d(x, y) < r} with the union of at most M balls of radius r/2. The base-2 logarit... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Metric space aimed at its subspace Summary Metric_space_aimed_at_its_subspace In mathematics, a metric space aimed at its subspace is a categorical construction that has a direct geometric meaning. It is also a useful step toward the construction of the metric envelope, or tight span, which are basic (injective) object... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Homogeneous metric Summary Finite_metric_space In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points. The distance is measured by a function called a metric or distance function. Metric spaces are the most general setting for studying many of the concepts... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Homogeneous metric Summary Finite_metric_space Other well-known examples are a sphere equipped with the angular distance and the hyperbolic plane. A metric may correspond to a metaphorical, rather than physical, notion of distance: for example, the set of 100-character Unicode strings can be equipped with the Hamming d... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Homogeneous metric Summary Finite_metric_space Since they are very general, metric spaces are a tool used in many different branches of mathematics. Many types of mathematical objects have a natural notion of distance and therefore admit the structure of a metric space, including Riemannian manifolds, normed vector spa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Hard analysis Metric spaces Classical_analysis > Important concepts > Metric spaces In mathematics, a metric space is a set where a notion of distance (called a metric) between elements of the set is defined. Much of analysis happens in some metric space; the most commonly used are the real line, the complex plane, Euc... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Microbundle Summary Microbundle In mathematics, a microbundle is a generalization of the concept of vector bundle, introduced by the American mathematician John Milnor in 1964. It allows the creation of bundle-like objects in situations where they would not ordinarily be thought to exist. For example, the tangent bundl... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Minimal K-type Summary Minimal_K-type In mathematics, a minimal K-type is a representation of a maximal compact subgroup K of a semisimple Lie group G that is in some sense the smallest representation of K occurring in a Harish-Chandra module of G. Minimal K-types were introduced by Vogan (1979) as part of an algebraic... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Minimal counterexample Summary Minimal_counterexample In mathematics, a minimal counterexample is the smallest example which falsifies a claim, and a proof by minimal counterexample is a method of proof which combines the use of a minimal counterexample with the ideas of proof by induction and proof by contradiction. M... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Minimal counterexample Summary Minimal_counterexample In which case, there may be multiple and more complex ways to structure the argument of the proof. The assumption that if there is a counterexample, there is a minimal counterexample, is based on a well-ordering of some kind. The usual ordering on the natural number... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Minimal surfaces Summary Minimal_surface_equation In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that minimized total surface ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Minimal surfaces of revolution Summary Minimal_surfaces_of_revolution In mathematics, a minimal surface of revolution or minimum surface of revolution is a surface of revolution defined from two points in a half-plane, whose boundary is the axis of revolution of the surface. It is generated by a curve that lies in the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Minimum bottleneck spanning tree Summary Minimum_bottleneck_spanning_tree In mathematics, a minimum bottleneck spanning tree (MBST) in an undirected graph is a spanning tree in which the most expensive edge is as cheap as possible. A bottleneck edge is the highest weighted edge in a spanning tree. A spanning tree is a ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mixed boundary condition Summary Mixed_boundary_condition In mathematics, a mixed boundary condition for a partial differential equation defines a boundary value problem in which the solution of the given equation is required to satisfy different boundary conditions on disjoint parts of the boundary of the domain where... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mock theta functions Summary Mock_theta_functions In mathematics, a mock modular form is the holomorphic part of a harmonic weak Maass form, and a mock theta function is essentially a mock modular form of weight 1/2. The first examples of mock theta functions were described by Srinivasa Ramanujan in his last 1920 lette... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Modular Lie algebra Summary Modular_Lie_algebra In mathematics, a modular Lie algebra is a Lie algebra over a field of positive characteristic. The theory of modular Lie algebras is significantly different from the theory of real and complex Lie algebras. This difference can be traced to the properties of Frobenius aut... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Modular equation Summary Modular_equation In mathematics, a modular equation is an algebraic equation satisfied by moduli, in the sense of moduli problems. That is, given a number of functions on a moduli space, a modular equation is an equation holding between them, or in other words an identity for moduli. The most f... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Modular equation Summary Modular_equation That implies that any two rational functions F and G, in the function field of the modular curve, will satisfy a modular equation P(F,G) = 0 with P a non-zero polynomial of two variables over the complex numbers. For suitable non-degenerate choice of F and G, the equation P(X,Y... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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