Eigenvalue

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 vector <math>\boldsymbol{x}\in\mathbb{R}</math> known as a eigenvector. The eigenvalue is the zero of a matrix's charateristic polynomial.

All the eigenvectors of a particular eigenvalue span a vector space called the eigenspace.