Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and the algebraic operations in terms of matrix addition and matrix multiplication.
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Basic Linear Algebra Subprograms
Basic Linear Algebra Subprograms (BLAS) is a de facto application programming interface standard for publishing libraries to perform basic linear algebra operations such as vector and matrix multiplication. They were first published in 1979, and are used to build larger packages such as LAPACK. Heavily used in high-performance computing, highly optimized implementations of the BLAS interface have been developed by hardware vendors such as Intel and AMD, as well as by other authors, e.g.
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Linear map
In mathematics, a linear map, linear mapping, linear transformation, or linear operator (in some contexts also called linear function) is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication. As a result, it always maps straight lines to straight lines or 0. The expression "linear operator" is commonly used for linear maps from a vector space to itself.
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Banach space
In mathematics, more specifically in functional analysis, a Banach space is a complete normed vector space. To elaborate, a Banach space is a vector space which is equipped with a norm and which is complete with respect to that norm. The definition of Banach spaces is as follows: A normed space is said to be Banach space if for every Cauchy sequence there exists an element such that .
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Finite element method
The finite element method (FEM) (its practical application often known as finite element analysis) is a numerical technique for finding approximate solutions of partial differential equations (PDE) as well as integral equations.
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Theory
The English word theory was derived from a technical term in philosophy in Ancient Greek. The word theoria, θεωρία, meant "a looking at, viewing, beholding", and referring to contemplation or speculation, as opposed to action. Theory is especially often contrasted to "practice" (from Greek praxis, πρᾶξις) a Greek term for "doing", which is opposed to theory because theory involved no doing apart from itself.
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Order (group theory)
In group theory, a branch of mathematics, the term order is used in two closely related senses: The order of a group is its cardinality, i.e. , the number of elements in its set. The order, sometimes period, of an element a of a group is the smallest positive integer m such that a = e (where e denotes the identity element of the group, and a denotes the product of m copies of a). If no such m exists, a is said to have infinite order. All elements of finite groups have finite order.
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Complexity
In general usage, complexity tends to be used to characterize something with many parts in intricate arrangement. The study of these complex linkages is the main goal of complex systems theory. In science there are at this time a number of approaches to characterizing complexity, many of which are reflected in this article. Neil Johnson describes complexity science as the study of the phenomena which emerge from a collection of interacting objects.
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