Characteristic polynomial

The characteristic polynomial of a square matrix 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} is given by,

$f(\lambda )=\det(A-\lambda I)$

where 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 I} is the identity matrix. The roots of this polynomial are the eigenvalues of the matrix.

The degree of this polynomial equals the length of the matrix's side. The number of roots therefore also equals this number, though some roots may be repeated.