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Michael Porter's generic strategies describe how a company can pursue competitive advantage across its chosen market scope. There are three generic strategies: lower cost, product differentiation, or focus. The focus strategy has two variants, cost focus and differentiation focus, so it is possible to see the concept i... | Wikipedia/Porter's_generic_strategies |
Quantum game theory is an extension of classical game theory to the quantum domain. It differs from classical game theory in three primary ways:
Superposed initial states,
Quantum entanglement of initial states,
Superposition of strategies to be used on the initial states.
This theory is based on the physics of inform... | Wikipedia/Quantum_game_theory |
Decision theory or the theory of rational choice is a branch of probability, economics, and analytic philosophy that uses expected utility and probability to model how individuals would behave rationally under uncertainty. It differs from the cognitive and behavioral sciences in that it is mainly prescriptive and conce... | Wikipedia/Statistical_decision_theory |
Appropriation is a process by which previously unowned natural resources, particularly land, become the property of a person or group of persons.
The term is widely used in economics in this sense.
In certain cases, it proceeds under very specifically defined forms, such as driving stakes or other such markers into the... | Wikipedia/First_possession_theory_of_property |
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathematics – is mostly concerned with those that are relevant to mathematics as a whole.
The modern study ... | Wikipedia/Axiomatic_set_theory |
In game theory and in particular the study of Blotto games and operational research, the Gibbs lemma is a result that is useful in maximization problems. It is named for Josiah Willard Gibbs.
Consider
ϕ
=
∑
i
=
1
... | Wikipedia/Gibbs_lemma |
In game theory, folk theorems are a class of theorems describing an abundance of Nash equilibrium payoff profiles in repeated games (Friedman 1971). The original Folk Theorem concerned the payoffs of all the Nash equilibria of an infinitely repeated game. This result was called the Folk Theorem because it was widely kn... | Wikipedia/Folk_theorem_(game_theory) |
Rationalizability is a solution concept in game theory. It is the most permissive possible solution concept that still requires both players to be at least somewhat rational and know the other players are also somewhat rational, i.e. that they do not play dominated strategies. A strategy is rationalizable if there exis... | Wikipedia/Rationalizable_strategy |
In game theory, perfect recall is a property of players within extensive-form games, introduced by Harold W. Kuhn in 1953. it describes a player's ability to remember their past actions and the information they possessed at previous decision points. For example, in a simplified card game where a player makes multiple b... | Wikipedia/Perfect_recall_(game_theory) |
In game theory, a max-dominated strategy is a strategy that is never a best response to any possible strategy profile of the other players. This means there is no situation in which the strategy is optimal to play, even if it is not strictly worse than another strategy in every case.
The concept generalizes the notion... | Wikipedia/Max-dominated_strategy |
Game theory is the study of participants' behavior in strategic situations.
Game theory may also refer to:
Game Theory (web show), an ongoing web series created and formerly hosted by Matthew Patrick
Combinatorial game theory, the study of move combinations in games like nim, chess, and go
Game Theory (band), a 1980s ... | Wikipedia/Game_theory_(disambiguation) |
In game theory, a strategy A dominates another strategy B if A will always produce a better result than B, regardless of how any other player plays. Some very simple games (called straightforward games) can be solved using dominance.
== Terminology ==
A player can compare two strategies, A and B, to determine which o... | Wikipedia/Iterated_elimination_of_dominated_strategies |
In game theory, a move, action, or play is any one of the options which a player can choose in a setting where the optimal outcome depends not only on their own actions but on the actions of others. The discipline mainly concerns the action of a player in a game affecting the behavior or actions of other players. Some ... | Wikipedia/Mixed_strategy |
In game theory, the traveler's dilemma (sometimes abbreviated TD) is a non-zero-sum game in which each player proposes a payoff. The lower of the two proposals wins; the lowball player receives the lowball payoff plus a small bonus, and the highball player receives the same lowball payoff, minus a small penalty. Surpri... | Wikipedia/Traveler's_dilemma |
In game theory, a non-cooperative game is a game in which there are no external rules or binding agreements that enforce the cooperation of the players. A non-cooperative game is typically used to model a competitive environment. This is stated in various accounts most prominent being John Nash's 1951 paper in the jour... | Wikipedia/Non-cooperative_game_theory |
A business model describes how a business organization creates, delivers, and captures value, in economic, social, cultural or other contexts. The model describes the specific way in which the business conducts itself, spends, and earns money in a way that generates profit. The process of business model construction an... | Wikipedia/Business_model |
Strategy (from Greek στρατηγία stratēgia, "troop leadership; office of general, command, generalship") is a general plan to achieve one or more long-term or overall goals under conditions of uncertainty. In the sense of the "art of the general", which included several subsets of skills including military tactics, siege... | Wikipedia/Strategy |
In game theory, the unscrupulous diner's dilemma (or just diner's dilemma) is an n-player prisoner's dilemma. The situation imagined is that several people go out to eat, and before ordering, they agree to split the cost equally between them. Each diner must now choose whether to order the costly or cheap dish. It is p... | Wikipedia/Unscrupulous_diner's_dilemma |
Theory of Games and Economic Behavior, published in 1944 by Princeton University Press, is a book by mathematician John von Neumann and economist Oskar Morgenstern which is considered the groundbreaking text that created the interdisciplinary research field of game theory. In the introduction of its 60th anniversary co... | Wikipedia/Theory_of_Games_and_Economic_Behavior |
In game theory, an information set is the basis for decision making in a game, which includes the actions available to players and the potential outcomes of each action. It consists of a collection of decision nodes that a player cannot distinguish between when making a move, due to incomplete information about previou... | Wikipedia/Information_set_(game_theory) |
Mechanism design (sometimes implementation theory or institution design) is a branch of economics and game theory. It studies how to construct rules—called mechanisms or institutions—that produce good outcomes according to some predefined metric, even when the designer does not know the players' true preferences or wha... | Wikipedia/Mechanism_design |
In game theory, a solution concept is a formal rule for predicting how a game will be played. These predictions are called "solutions", and describe which strategies will be adopted by players and, therefore, the result of the game. The most commonly used solution concepts are equilibrium concepts, most famously Nash e... | Wikipedia/Solution_concept |
Behavioral game theory seeks to examine how people's strategic decision-making behavior is shaped by social preferences, social utility and other psychological factors. Behavioral game theory analyzes interactive strategic decisions and behavior using the methods of game theory, experimental economics, and experimental... | Wikipedia/Behavioural_game_theory |
In the field of management, strategic management involves the formulation and implementation of the major goals and initiatives taken by an organization's managers on behalf of stakeholders, based on consideration of resources and an assessment of the internal and external environments in which the organization operat... | Wikipedia/Strategic_management |
Prim–Read theory, or Prim–Read defense, was an important development in game theory that led to radical changes in the United States' views on the value of anti-ballistic missile (ABM) systems. The theory assigns a certain cost to deploying defensive missiles and suggests a way to maximize their value in terms of the a... | Wikipedia/Prim–Read_theory |
The Hamilton-Jacobi-Bellman (HJB) equation is a nonlinear partial differential equation that provides necessary and sufficient conditions for optimality of a control with respect to a loss function. Its solution is the value function of the optimal control problem which, once known, can be used to obtain the optimal co... | Wikipedia/Hamilton–Jacobi–Bellman_equation |
Combinatorial Games: Tic-Tac-Toe Theory is a monograph on the mathematics of tic-tac-toe and other positional games, written by József Beck. It was published in 2008 by the Cambridge University Press as volume 114 of their Encyclopedia of Mathematics and its Applications book series (ISBN 978-0-521-46100-9).
== Topic... | Wikipedia/Combinatorial_Games:_Tic-Tac-Toe_Theory |
Cognitive science is the interdisciplinary, scientific study of the mind and its processes. It examines the nature, the tasks, and the functions of cognition (in a broad sense). Mental faculties of concern to cognitive scientists include perception, memory, attention, reasoning, language, and emotion. To understand the... | Wikipedia/Cognitive_science |
Mean-field game theory is the study of strategic decision making by small interacting agents in very large populations. It lies at the intersection of game theory with stochastic analysis and control theory. The use of the term "mean field" is inspired by mean-field theory in physics, which considers the behavior of sy... | Wikipedia/Mean-field_game_theory |
In game theory, Zermelo's theorem is a theorem about finite two-person games of perfect information in which the players move alternately and in which chance does not affect the decision making process. It says that if the game cannot end in a draw, then one of the two players must have a winning strategy (i.e. can for... | Wikipedia/Zermelo's_theorem_(game_theory) |
Dispute resolution or dispute settlement is the process of resolving disputes between parties. The term dispute resolution is conflict resolution through legal means.
Prominent venues for dispute settlement in international law include the International Court of Justice (formerly the Permanent Court of International J... | Wikipedia/Dispute_resolution |
In game theory, a focal point (or Schelling point) is a solution that people tend to choose by default in the absence of communication in order to avoid coordination failure. The concept was introduced by the American economist Thomas Schelling in his book The Strategy of Conflict (1960). Schelling states that "[p]eopl... | Wikipedia/Focal_point_(game_theory) |
A business can use a variety of pricing strategies when selling a product or service. To determine the most effective pricing strategy for a company, senior executives need to first identify the company's pricing position, pricing segment, pricing capability and their competitive pricing reaction strategy. Pricing stra... | Wikipedia/Pricing_strategy |
In management, a strategy map is a diagram that documents the strategic goals being pursued by an organization or management team. It is an element of the documentation associated with the Balanced Scorecard, and in particular is characteristic of the second generation of Balanced Scorecard designs that first appeared ... | Wikipedia/Strategy_map |
In mathematics, the replicator equation is a type of dynamical system used in evolutionary game theory to model how the frequency of strategies in a population changes over time. It is a deterministic, monotone, non-linear, and non-innovative dynamic that captures the principle of natural selection in strategic interac... | Wikipedia/Replicator_equation |
An economic model is a theoretical construct representing economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified, often mathematical, framework designed to illustrate complex processes. Frequently, economic models posit structural... | Wikipedia/Economic_model |
Strategic thinking is a mental or thinking process applied by individuals and within organizations in the context of achieving a goal or set of goals.
When applied in an organizational strategic management process, strategic thinking involves the generation and application of unique business insights and opportunities ... | Wikipedia/Strategic_thinking |
Porter's Five Forces Framework is a method of analysing the competitive environment of a business. It draws from industrial organization (IO) economics to derive five forces that determine the competitive intensity and, therefore, the attractiveness (or lack thereof) of an industry in terms of its profitability. An "un... | Wikipedia/Porter's_five_forces_analysis |
Algorithmic game theory (AGT) is an interdisciplinary field at the intersection of game theory and computer science, focused on understanding and designing algorithms for environments where multiple strategic agents interact. This research area combines computational thinking with economic principles to address challen... | Wikipedia/Algorithmic_game_theory |
Game Theory was an American power pop band, founded in 1982 by singer/songwriter Scott Miller, combining melodic jangle pop with dense experimental production and hyperliterate lyrics. MTV described their sound as "still visceral and vital" in 2013, with records "full of sweetly psychedelic-tinged, appealingly idiosync... | Wikipedia/Game_Theory_(band) |
The foundations of negotiation theory are decision analysis, behavioral decision-making, game theory, and negotiation analysis.
Another classification of theories distinguishes between Structural Analysis, Strategic Analysis, Process Analysis, Integrative Analysis, and behavioral analysis of negotiations.
Negotiation i... | Wikipedia/Negotiation_theory |
Algorithmic mechanism design (AMD) lies at the intersection of economic game theory, optimization, and computer science. The prototypical problem in mechanism design is to design a system for multiple self-interested participants, such that the participants' self-interested actions at equilibrium lead to good system pe... | Wikipedia/Algorithmic_mechanism_design |
In philosophy of science, idealization is the process by which scientific models assume facts about the phenomenon being modeled that are strictly false but make models easier to understand or solve. That is, it is determined whether the phenomenon approximates an "ideal case," then the model is applied to make a predi... | Wikipedia/Idealization_(science_philosophy) |
In game theory, the outcome of a game is the ultimate result of a strategic interaction with one or more people, dependant on the choices made by all participants in a certain exchange. It represents the final payoff resulting from a set of actions that individuals can take within the context of the game. Outcomes are ... | Wikipedia/Outcome_(game_theory) |
Strategic planning is the activity undertaken by an organization through which it seeks to define its future direction and makes decisions such as resource allocation aimed at achieving its intended goals. "Strategy" has many definitions, but it generally involves setting major goals, determining actions to achieve the... | Wikipedia/Strategic_planning |
The pirate game is a simple mathematical game. It is a multi-player version of the ultimatum game.
== The game ==
There are five rational pirates (in strict decreasing order of seniority A, B, C, D and E) who found 100 gold coins. They must decide how to distribute them.
The pirate world's rules of distribution say t... | Wikipedia/Pirate_game |
The labor theory of property, also called the labor theory of appropriation, labor theory of ownership, labor theory of entitlement, and principle of first appropriation, is a theory of natural law that holds that property originally comes about by the exertion of labor upon natural resources. The theory has been used ... | Wikipedia/Labor_theory_of_property |
Proponents of democratic peace theory argue that both electoral and republican forms of democracy are hesitant to engage in armed conflict with other identified democracies. Different advocates of this theory suggest that several factors are responsible for motivating peace between democratic states. Individual theoris... | Wikipedia/Democratic_peace_theory |
In computer science, an online algorithm is one that can process its input piece-by-piece in a serial fashion, i.e., in the order that the input is fed to the algorithm, without having the entire input available from the start. In contrast, an offline algorithm is given the whole problem data from the beginning and is ... | Wikipedia/Online_algorithm |
Alternative dispute resolution (ADR), or external dispute resolution (EDR), typically denotes a wide range of dispute resolution processes and techniques that parties can use to settle disputes with the help of a third party. They are used for disagreeing parties who cannot come to an agreement short of litigation. How... | Wikipedia/Alternative_dispute_resolution |
Demographic economics or population economics is the application of economic analysis to demography, the study of human populations, including size, growth, density, distribution, and vital statistics.
== Aspects ==
Aspects of the subject include:
marriage and fertility
the family
divorce
morbidity and life expectan... | Wikipedia/Demographic_economics |
In fair division problems, spite is a phenomenon that occurs when a player's value of an allocation decreases when one or more other players' valuation increases. Thus, other things being equal, a player exhibiting spite will prefer an allocation in which other players receive less than more (if more of the good is de... | Wikipedia/Spite_(game_theory) |
Optimal control theory is a branch of control theory that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with con... | Wikipedia/Optimal_control |
In economics and game theory, the decisions of two or more players are called strategic complements if they mutually reinforce one another, and they are called strategic substitutes if they mutually offset one another. These terms were originally coined by Bulow, Geanakoplos, and Klemperer (1985).
To see what is meant... | Wikipedia/Strategic_complements |
In game theory, and particularly mechanism design, participation constraints or individual rationality constraints are said to be satisfied if a mechanism leaves all participants at least as well-off as they would have been if they hadn't participated.
In terms of information structure, there are 3 types of Participati... | Wikipedia/Participation_constraint_(mechanism_design) |
Deterrence theory refers to the scholarship and practice of how threats of using force by one party can convince another party to refrain from initiating some other course of action. The topic gained increased prominence as a military strategy during the Cold War with regard to the use of nuclear weapons and is related... | Wikipedia/Deterrence_theory |
The strategic grid model is a contingency approach that can be used to determine the strategic relevance of IT to an organization. The model was proposed by F. Warren McFarlan and James L. McKenney in 1983, and takes the impact of the information technology on the strategy in future planning as the horizontal axis, and... | Wikipedia/Strategic_Grid_Model |
Rational choice modeling refers to the use of decision theory (the theory of rational choice) as a set of guidelines to help understand economic and social behavior. The theory tries to approximate, predict, or mathematically model human behavior by analyzing the behavior of a rational actor facing the same costs and b... | Wikipedia/Rational_agent_model |
In game theory, a strategy A dominates another strategy B if A will always produce a better result than B, regardless of how any other player plays. Some very simple games (called straightforward games) can be solved using dominance.
== Terminology ==
A player can compare two strategies, A and B, to determine which o... | Wikipedia/Dominant_strategy |
Behavioral strategy is an interdisciplinary field within strategic management that integrates insights from psychology, behavioral economics, and cognitive science to better understand how individuals and groups make strategic decisions. It challenges the assumptions of traditional economic models that presume perfect ... | Wikipedia/Behavioral_strategy |
In combinatorial game theory, the strategy-stealing argument is a general argument that shows, for many two-player games, that the second player cannot have a guaranteed winning strategy. The strategy-stealing argument applies to any symmetric game (one in which either player has the same set of available moves with th... | Wikipedia/Strategy_stealing_argument |
Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed two-person zero-sum games, in which a participant's gains or losses are exa... | Wikipedia/Strategic_interaction |
Strategic studies is an interdisciplinary academic field centered on the study of peace and conflict strategies, often devoting special attention to the relationship between military history, international politics, geostrategy, international diplomacy, international economics, and military power. In the scope of the ... | Wikipedia/Strategic_studies |
In cooperative game theory, the core is the set of feasible allocations or imputations where no coalition of agents can benefit by breaking away from the grand coalition. One can think of the core corresponding to situations where it is possible to sustain cooperation among all agents. A coalition is said to improve u... | Wikipedia/Core_(game_theory) |
Conflict resolution is conceptualized as the methods and processes involved in facilitating the peaceful ending of conflict and retribution. Committed group members attempt to resolve group conflicts by actively communicating information about their conflicting motives or ideologies to the rest of group (e.g., intentio... | Wikipedia/Conflict_resolution |
Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Research in this field has primarily focused on two-player games in which a position evolves through alternating moves, each governed by well-defined rules, with the ai... | Wikipedia/Combinatorial_Game_Theory |
Compositional game theory is a branch of game theory and computer science, which aims to present large complex games as a composition of simple small games.
== Motivation ==
A major theme in computer science is the ability to construct simple building-blocks (e.g. functions or procedures in a programming language), a... | Wikipedia/Compositional_game_theory |
The business model canvas is a strategic management template that is used for developing new business models and documenting existing ones. It offers a visual chart with elements describing a firm's or product's value proposition, infrastructure, customers, and finances, assisting businesses to align their activities b... | Wikipedia/Business_Model_Canvas |
The term conceptual model refers to any model that is formed after a conceptualization or generalization process. Conceptual models are often abstractions of things in the real world, whether physical or social. Semantic studies are relevant to various stages of concept formation. Semantics is fundamentally a study of ... | Wikipedia/Conceptual_model |
Theory of Games and Economic Behavior, published in 1944 by Princeton University Press, is a book by mathematician John von Neumann and economist Oskar Morgenstern which is considered the groundbreaking text that created the interdisciplinary research field of game theory. In the introduction of its 60th anniversary co... | Wikipedia/Theory_of_games_and_economic_behavior |
In mathematics, Sperner's lemma is a combinatorial result on colorings of triangulations, analogous to the Brouwer fixed point theorem, which is equivalent to it. It states that every Sperner coloring (described below) of a triangulation of an
n
{\displaystyle n}
-dimensional ... | Wikipedia/Sperner's_lemma |
A weak evolutionarily stable strategy (WESS) is a more broad form of evolutionarily stable strategy (ESS). Like ESS, a WESS is able to defend against an invading "mutant" strategy. This means the WESS cannot be entirely eliminated from the population.
The definition of WESS is similar to ESS. Any strategy s is a weakly... | Wikipedia/Weak_evolutionarily_stable_strategy |
The black swan theory or theory of black swan events is a metaphor that describes an event that comes as a surprise, has a major effect, and is often inappropriately rationalized after the fact with the benefit of hindsight. The term arose from Latin expression which was based on the presumption that black swans did no... | Wikipedia/Black_swan_theory |
In operations research, drama theory is one of several problem structuring methods. It is based on game theory and adapts the use of games to complex organisational situations, accounting for emotional responses that can provoke irrational reactions and lead the players to redefine the game. In a drama, emotions trigge... | Wikipedia/Drama_theory |
Behavioral game theory seeks to examine how people's strategic decision-making behavior is shaped by social preferences, social utility and other psychological factors. Behavioral game theory analyzes interactive strategic decisions and behavior using the methods of game theory, experimental economics, and experimental... | Wikipedia/Behavioral_game_theory |
An Economic Theory of Democracy is a treatise of economics written by Anthony Downs, published in 1957. The book set forth a model with precise conditions under which economic theory could be applied to non-market political decision-making. It also suggested areas of empirical research that could be tested to confirm... | Wikipedia/An_Economic_Theory_of_Democracy |
Mean-field game theory is the study of strategic decision making by small interacting agents in very large populations. It lies at the intersection of game theory with stochastic analysis and control theory. The use of the term "mean field" is inspired by mean-field theory in physics, which considers the behavior of sy... | Wikipedia/Mean_field_game_theory |
An evolutionarily stable strategy (ESS) is a strategy (or set of strategies) that is impermeable when adopted by a population in adaptation to a specific environment, that is to say it cannot be displaced by an alternative strategy (or set of strategies) which may be novel or initially rare. Introduced by John Maynard ... | Wikipedia/Evolutionarily_stable_strategy |
In combinatorial game theory, star, written as ∗ or ∗1, is the value given to the game where both players have only the option of moving to the zero game. Star may also be denoted as the surreal form {0|0}. This game is an unconditional first-player win.
Star, as defined by John Conway in Winning Ways for your Mathemat... | Wikipedia/Star_(game_theory) |
In economics, industrial organization is a field that builds on the theory of the firm by examining the structure of (and, therefore, the boundaries between) firms and markets. Industrial organization adds real-world complications to the perfectly competitive model, complications such as transaction costs, limited info... | Wikipedia/Industrial_organization |
Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Research in this field has primarily focused on two-player games in which a position evolves through alternating moves, each governed by well-defined rules, with the ai... | Wikipedia/Combinatorial_game_theory |
In combinatorial game theory, the strategy-stealing argument is a general argument that shows, for many two-player games, that the second player cannot have a guaranteed winning strategy. The strategy-stealing argument applies to any symmetric game (one in which either player has the same set of available moves with th... | Wikipedia/Strategy-stealing_argument |
In game theory, normal form is a description of a game. Unlike extensive form, normal-form representations are not graphical per se, but rather represent the game by way of a matrix. While this approach can be of greater use in identifying strictly dominated strategies and Nash equilibria, some information is lost as c... | Wikipedia/Strategic_form |
In game theory, a move, action, or play is any one of the options which a player can choose in a setting where the optimal outcome depends not only on their own actions but on the actions of others. The discipline mainly concerns the action of a player in a game affecting the behavior or actions of other players. Some ... | Wikipedia/Strategy_(game_theory) |
In combinatorial game theory, the paranoid algorithm is a game tree search algorithm designed to analyze multi-player games using a two-player adversarial framework. The algorithm assumes all opponents form a coalition to minimize the focal player’s payoff, transforming an n-player non-zero-sum game into a zero-sum gam... | Wikipedia/Paranoid_algorithm |
The volunteer's dilemma is a game that models a situation in which each player can either make a small sacrifice that benefits everybody, or instead wait in hope of benefiting from someone else's sacrifice.
One example is a scenario in which the electricity supply has failed for an entire neighborhood. All inhabitants ... | Wikipedia/Volunteer's_dilemma |
In multilinear algebra, the tensor rank decomposition or rank-R decomposition is the decomposition of a tensor as a sum of R rank-1 tensors, where R is minimal. Computing this decomposition is an open problem.
Canonical polyadic decomposition (CPD) is a variant of the tensor rank decomposition, in which the tensor is ... | Wikipedia/Tensor_rank_decomposition |
Controllability is an important property of a control system and plays a crucial role in many regulation problems, such as the stabilization of unstable systems using feedback, tracking problems, obtaining optimal control strategies, or, simply prescribing an input that has a desired effect on the state.
Controllabilit... | Wikipedia/Controllability |
In linear algebra, the nonnegative rank of a nonnegative matrix is a concept similar to the usual linear rank of a real matrix, but adding the requirement that certain coefficients and entries of vectors/matrices have to be nonnegative.
For example, the linear rank of a matrix is the smallest number of vectors, such th... | Wikipedia/Nonnegative_rank_(linear_algebra) |
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There are many types of tensors, including scalars and vectors (which ar... | Wikipedia/Tensors |
The Steinitz exchange lemma is a basic theorem in linear algebra used, for example, to show that any two bases for a finite-dimensional vector space have the same number of elements. The result is named after the German mathematician Ernst Steinitz. The result is often called the Steinitz–Mac Lane exchange lemma, also ... | Wikipedia/Steinitz_exchange_lemma |
In mathematics, the modern component-free approach to the theory of a tensor views a tensor as an abstract object, expressing some definite type of multilinear concept. Their properties can be derived from their definitions, as linear maps or more generally; and the rules for manipulations of tensors arise as an exten... | Wikipedia/Simple_tensor |
In mathematics, the modern component-free approach to the theory of a tensor views a tensor as an abstract object, expressing some definite type of multilinear concept. Their properties can be derived from their definitions, as linear maps or more generally; and the rules for manipulations of tensors arise as an exten... | Wikipedia/Tensor_rank |
In mathematics, specifically linear algebra, a degenerate bilinear form f (x, y ) on a vector space V is a bilinear form such that the map from V to V∗ (the dual space of V ) given by v ↦ (x ↦ f (x, v )) is not an isomorphism. An equivalent definition when V is finite-dimensional is that it has a non-trivial kernel: t... | Wikipedia/Degenerate_form |
A monograph is generally a long-form work on one (usually scholarly) subject, or one aspect of a subject, typically created by a single author or artist (or, sometimes, by two or more authors). Traditionally it is in written form and published as a book, but it may be an artwork, audiovisual work, or exhibition made up... | Wikipedia/Monograph |
In mathematics, an algebraic equation or polynomial equation is an equation of the form
P
=
0
{\displaystyle P=0}
, where P is a polynomial with coefficients in some field, often the field of the rational numbers.
For example,
... | Wikipedia/Algebraic_equations |
Natural science or empirical science is one of the branches of science concerned with the description, understanding and prediction of natural phenomena, based on empirical evidence from observation and experimentation. Mechanisms such as peer review and reproducibility of findings are used to try to ensure the validit... | Wikipedia/Natural_sciences |
In abstract algebra, a branch of mathematics, a simple ring is a non-zero ring that has no two-sided ideal besides the zero ideal and itself. In particular, a commutative ring is a simple ring if and only if it is a field.
The center of a simple ring is necessarily a field. It follows that a simple ring is an associati... | Wikipedia/Simple_algebra |
Abstrakt Algebra was a Swedish experimental metal band with influences from power metal and doom metal. It was founded by bassist Leif Edling in 1994, shortly after his main project Candlemass split up.
They made one album, but Edling had already started working on a second album with a different line-up. However, due ... | Wikipedia/Abstrakt_Algebra |
In quantum field theory, a force carrier is a type of particle that gives rise to forces between other particles. They serve as the quanta of a particular kind of physical field. Force carriers are also known as messenger particles, intermediate particles, or exchange particles.
== Particle and field viewpoints ==
Q... | Wikipedia/Force_carrier |
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