Linear algebra is a branch of mathematics, and its research objects are vectors, vector spaces (or linear spaces), linear transformations and linear equations with finite dimensions. Vector space is an important subject in modern mathematics. Therefore, linear algebra is widely used in abstract algebra and functional analysis; Through analytic geometry, linear algebra can be expressed concretely.

The theory of linear algebra has been extended to operator theory. Because the nonlinear model in scientific research can usually be approximated as a linear model, linear algebra is widely used in natural science and social science.

As an independent branch discipline, linear algebra has a long history, although it was only formed in the 20th century. The problem of "chicken and rabbit in the same cage" is actually a simple problem of solving linear equations. The oldest linear problem is the solution of linear equations, which has been completely described in the ancient Chinese mathematical work "Nine Chapters Arithmetic Equations", and the method in it is essentially equivalent to the elementary transformation of rows of the augmented matrix of modern equations and the method of eliminating unknowns.

Due to the work of Fermat and Descartes, linear algebra in the modern sense basically appeared in the seventeenth century. Until the end of18th century, the field of linear algebra was limited to plane and space. /kloc-completed the transition to n-dimensional linear space in the first half of the 9th century.