Linear algebra

Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps (or linear transformations or linear operators) and can be represented by matrices if a basis is given. Thus matrix theory is often considered as a part of linear algebra. Linear algebra is commonly restricted to the case of finite dimensional vector spaces, while the peculiarities of the infinite dimensional case are traditionally covered in linear functional analysis.
Linear algebra is central to modern mathematics and its applications. An elementary application of linear algebra is to find the solution of a system of linear equations in several unknowns. More advanced applications are ubiquitous in areas as diverse as abstract algebra and functional analysis. Linear algebra has a concrete representation in analytic geometry and is generalized in operator theory and in module theory. It has extensive applications in e

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