# Norm

A norm is a quantity that describes the length, size, or extent of a mathematical object.

Norm is a college-level concept that would be first encountered in a linear algebra course.

### Examples

Absolute Value: | The absolute value of a number is the distance of the number from the origin. |

### Prerequisites

Inner Product: | (1) In a vector space, an inner product is a way to multiply vectors together, with the result being a scalar. (2) In vector algebra, the term inner product is used as a synonym for dot product. |

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. |

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. |