Difference between revisions of "Characteristic polynomial"
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| − | The '''characteristic polynomial''' of a [[matrix]] <math>A</math> is given by, | + | The '''characteristic polynomial''' of a square [[matrix]] <math>A</math> is given by, |
| − | :<math> | + | :<math>f(\lambda) = \det(A-\lambda I)</math> |
| − | where <math>I</math> is the [[identity matrix]]. | + | where <math>I</math> is the [[identity matrix]]. The zeros of this polynomial are the eigenvalues of the matrix. |
[[Category:Linear algebra]] | [[Category:Linear algebra]] | ||
Revision as of 01:13, July 4, 2008
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 zeros of this polynomial are the eigenvalues of the matrix.