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 $\lambda$ such that

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

for some non-zero vector ${\boldsymbol {x}}\in \mathbb {R}$ known as a eigenvector. The eigenvalue is the zero of a matrix's charateristic polynomial.

The span of all the eigenvectors corresponding to a fixed eigenvalue 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} is called the eigenspace 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 E_\lambda} of 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 A} .