Linear Algebra

Linear algebra is the branch of mathematics concerning vector spaces, often finite or countably infinite dimensional, as well as linear mappings between such spaces. Such an investigation is initially motivated by a system of linear equations in several unknowns. Such equations are naturally represented using the formalism of matrices and vectors.

Linear algebra is central to both pure and applied mathematics. For instance, abstract algebra arises by relaxing the axioms of a vector space, leading to a number of generalizations. Functional analysis studies the infinite-dimensional version of the theory of vector spaces. Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations. Techniques from linear algebra are also used in analytic geometry, engineering, physics, natural sciences, computer science, and the social sciences (particularly in economics). Because linear algebra is such a well-developed theory, nonlinear mathematical models are sometimes approximated by linear ones.

Read more about Linear AlgebraHistory, Some Main Useful Theorems, Applications, Generalizations and Related Topics

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Linear Algebra - Generalizations and Related Topics
... Since linear algebra is a successful theory, its methods have been developed and generalized in other parts of mathematics ... The concepts of linear independence, span, basis, and dimension (which is called rank in module theory) still make sense ... Nevertheless, many theorems from linear algebra become false in module theory ...
Super Linear Algebra - Scope of Study - Linear Transformations
... Similarly as in the theory of other algebraic structures, linear algebra studies mappings between vector spaces that preserve the vector-space structure ... two vector spaces V and W over a field F, a linear transformation (also called linear map, linear mapping or linear operator) is a map that is compatible with addition and scalar ... When a bijective linear mapping exists between two vector spaces (that is, every vector from the second space is associated with exactly one in the first), we say that the two spaces are ...
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... It has numerical packages for linear algebra and non-linear optimization ... Efficient Java Matrix Library (EJML) is an open-source linear algebra library for manipulating dense matrices ... JAMA, a numerical linear algebra toolkit for the Java programming language ...
Armadillo (C++ Library)
... aims to provide an efficient and streamlined base for linear algebra operations (matrix maths), while at the same time having a straightforward and easy to use interface ... Various matrix decompositions are provided through optional integration with Linear Algebra PACKage (LAPACK) and Automatically Tuned Linear Algebra Software (ATLAS) libraries ... Armadillo is related to the Boost Basic Linear Algebra Subprograms (uBLAS) library, but has a more accessible syntax ...
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... numerical array classes and functions for general math, FFT and linear algebra, aims.NET/mono, 64 ... bit, script-like syntax in C#, 2D 3D plot controls, efficient memory management IMSL ... component libraries for the.NET platform, including signal processing (FFT) classes, a linear algebra (LAPACK BLAS) framework, and a statistics package ... is a large collection of numerical algorithms including linear algebra, (advanced) optimization, interpolation, Markov model, principal component analysis, time series analysis, hypothesis testing, regressions ...

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