# 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.

Matrix 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.

### Examples

Rotation Matrix: | A rotation matrix is a matrix that corresponds to the linear transformation of a rotation. |

### Prerequisites

Linear Algebra: | Linear algebra is study of linear systems of equations and their transformation properties. |

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. |

Vector: | (1) In vector algebra, a vector mathematical entity that has both magnitude (which can be zero) and direction. (2) In topology, a vector is an element of a vector space. |

Vector Space: | A vector space is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space. |