What is linear algebra?

  • (noun): The part of algebra that deals with the theory of linear equations and linear transformation.

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.

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List Of Numerical Libraries - .NET Framework Languages C#, F# and VB.NET
... 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 ... 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 ...
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 ... Given 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 ... 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 isomorphic ...
List Of Numerical Libraries - Java
... 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)
... 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 ... matrix decompositions are provided through optional integration with Linear Algebra PACKage (LAPACK) and Automatically Tuned Linear Algebra Software (ATL ... Armadillo is related to the Boost Basic Linear Algebra Subprograms (uBLAS) library, but has a more accessible syntax ...
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 ...

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