# Determinant

The determinant of a square matrix is a scalar (commonly computed using so-called expansion by minors) which is nonzero if and only if the matrix has an inverse.

Determinant is a high school-level concept that would be first encountered in a pre-calculus course. It is listed in the California State Standards for Linear Algebra.

### Prerequisites

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 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. |