Linear algebra is a branch of mathematics that deals with the study of linear equations, matrices, vectors, and their properties. It is a fundamental tool in many areas of science, engineering, and mathematics, including computer graphics, physics, economics, and statistics.

Linear algebra involves the study of linear transformations, which are functions that map vectors from one space to another. These transformations can be represented by matrices, which are rectangular arrays of numbers that encode the linear transformation.

The study of linear algebra includes topics such as vector spaces, linear independence, basis and dimension, eigenvalues and eigenvectors, determinants, and inner products. These concepts are used to solve systems of linear equations, find the inverse of matrices, and analyze the behavior of linear systems.

Linear algebra has many applications in real-world problems, such as image processing, data analysis, and machine learning. It is also a foundational subject for advanced mathematics, including abstract algebra, functional analysis, and differential equations.