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Characteristic polynomial (view source)
Revision as of 23:56, February 22, 2023
, 23:56, February 22, 2023no edit summary
:<math>f(\lambda) = \det(A-\lambda I)</math>
:<math>f(\lambda) = \det(A-\lambda I)</math>
where <math>I</math> is the [[identity matrix]]. The [[root]]s of this [[polynomial]] are the [[eigenvalue]]s of the matrix.
where <math>I</math> is the [[identity matrix]]. The [[root (Mathematics)|root]]s of this [[polynomial]] are the [[eigenvalue]]s of the matrix.
The degree of this polynomial equals the length of the matrix's side. The number of roots therefore is not greater than this number.
The degree of this polynomial equals the length of the matrix's side. The number of roots therefore is not greater than this number.