# Linear Algebra

**Linear algebra** is the branch of mathematics concerning linear equations, linear maps and their representations in vector spaces and through matrices.

There is a strong relationship between linear algebra and geometry, which started with the introduction by René Descartes, in 1637, of Cartesian coordinates.

In this new (at that time) geometry, now called Cartesian geometry, points are represented by Cartesian coordinates, which are sequences of three real numbers (in the case of the usual three-dimensional space).

The basic objects of geometry, which are lines and planes are represented by linear equations.

Thus, computing intersections of lines and planes amounts to solving systems of linear equations.

This was one of the main motivations for developing linear algebra.