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# What is linear algebra? What is matrix algebra?

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What is linear algebra? What is matrix algebra?

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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 a linear one.

Matrix is a rectangular table of numbers or, more generally, a table consisting of abstract quantities that can be added and multiplied. Matrices are used to describe linear equations, keep track of the coefficients of linear transformations and to record data that depend on two parameters. Matrices can be added, multiplied, and decomposed in various ways, making them a key concept in linear algebra and matrix theory. Matrix algebra is a branch of algebra that deals with matrices.

Reference:
http://www.xycoon.com/matrix_algebra.htm
http://www.maths.mq.edu.au/~wchen/lnlafolder/lnla.html

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