# Linear algebra

**Linear algebra** is a branch of mathematics encompassing a broad range of topics, such as systems of linear equations, matrix algebra, and arrows in Cartesian two-dimensional or three-dimensional space (appearing, for instance, as forces in physics). More generally, the study of all of these topics can be systematized into the theory of vector spaces.

Linear algebra has a vast range of applications, in part because of the ubiquity of systems of linear equations in scientific models and real-world problems. Other topics in linear algebra, such as matrix algebra, eigenvalues and eigenvectors, linear operators, matrix representations, and inner products find broad application in science.

Linear algebra is an essential tool in other mathematical fields, such as differential equations theory, functional analysis, and differential geometry.