Difference between revisions of "Characteristic polynomial"
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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]]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 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. |
[[Category:Linear algebra]] | [[Category:Linear algebra]] | ||
Revision as of 21:50, May 2, 2010
The characteristic polynomial of a square matrix <math>A</math> is given by,
- <math>f(\lambda) = \det(A-\lambda I)</math>
where <math>I</math> 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.