Eigenvalue

It has been suggested that this article or section be merged with [[::eigenvector|eigenvector]]. (Discuss)

An eigenvalue of a square matrix <math>A</math> is a complex number <math>\lambda</math> such that

<math>A\boldsymbol{x}=\lambda\boldsymbol{x}</math>

for some non-zero vector <math>\boldsymbol{x}\in\mathbb{R}</math> known as a eigenvector. The eigenvalue is the zero of a matrix's charateristic polynomial, the degree of the corresponding root is called the algebraic multiplicity of the eigenvalue.

The span of all the eigenvectors corresponding to a fixed eigenvalue <math>\lambda</math> is called the eigenspace <math>E_\lambda</math> of <math>A</math>.