Linear algebra
 

Linear algebra is central to almost all areas of mathematics.
For instance, linear algebra is fundamental in modern presentations of geometry,
including for defining basic objects such as lines, planes and rotations.

Also, functional analysis, a branch of mathematical analysis,
may be viewed as basically the application of linear algebra to spaces of functions.

Linear algebra is also used in most sciences and fields of engineering,
because it allows modeling many natural phenomena,
and computing efficiently with such models.