Linear algebra is a branch of algebra, which mainly deals with linear relations. Linear relationship means that the relationship between mathematical objects is expressed in linear form. For example, in analytic geometry, the equation of a straight line on the plane is a binary linear equation; The equation of spatial plane is a three-dimensional linear equation, and the spatial straight line is regarded as the intersection of two planes.

It is expressed by an equation group composed of two ternary linear equations. A linear equation with n unknowns is called a linear equation. Functions whose variables are linear are called linear functions. Linear relation problem is called linear problem for short. The problem of solving linear equations is the simplest linear problem.

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.