**Linear algebra** is the branch of mathematics concerned with the study of vectors, vector spaces (also called *linear spaces*), linear maps (also called *linear transformations*), and systems of linear equations. Vector spaces are a central theme in modern mathematics; thus, linear algebra is widely used in both abstract algebra and functional analysis. Linear algebra also has a concrete representation in analytic geometry and it is generalized in operator theory. It has extensive applications in the natural sciences and the social sciences, since nonlinear models can often be approximated by linear ones.

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