Difference between revisions of "Characteristic polynomial"
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m (sysops are not wrong) |
(number of roots may be smaller than degree of the 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 number of roots therefore | + | The degree of this polynomial equals the length of the matrix's side. The number of roots therefore is not greater than this number. |
[[Category:Linear algebra]] | [[Category:Linear algebra]] | ||
Revision as of 15:12, June 1, 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 is not greater than this number.