Eigenvalue

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

An eigenvalue of a square matrix $A$ is a complex number Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lambda} such that

$A{\boldsymbol {x}}=\lambda {\boldsymbol {x}}$

for some non-zero vector Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \boldsymbol{x}\in\mathbb{R}} 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.