# Eigenvalue

An eigenvalue is one of a set of special scalars associated with a linear system of equations that describes that system's fundamental modes.

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

### 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. |

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. |