**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 Algebra: History, Some Main Useful Theorems, Applications, Generalizations and Related Topics

### Other articles related to "linear algebra, linear":

... 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 (ATLAS ... Due to its approach, Armadillo is related to the Boost Basic

**Linear Algebra**Subprograms (uBLAS) library, but has a more accessible syntax ...

... It has numerical packages for

**linear algebra**and non-

**linear**optimization ... 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 ...

... high performance, typesafe 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 ... 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 ...

**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 ...

**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 compatible with ... 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 ...

### Famous quotes containing the word algebra:

“Poetry has become the higher *algebra* of metaphors.”

—José Ortega Y Gasset (1883–1955)