# Matrix Multiplication

Matrix multiplication is the process of multiplying two matrices (each of which represents a linear transformation), which forms a new matrix corresponding to the matrix representation of the two transformations' composition.

Matrix multiplication is a high school-level concept that would be first encountered in a linear algebra course. It is listed in the California State Standards for Linear Algebra.

### Prerequisites

Linear Transformation: | A function from one vector space to another. If bases are chosen for the vector spaces, a linear transformation can be given by a matrix. |

Matrix: | A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, for every linear transformation, there exists exactly one corresponding matrix, and every matrix corresponds to a unique linear transformation. The matrix is an extremely important concept in linear algebra. |