Faddeev–LeVerrier algorithm: Difference between revisions

Revision as of 21:41, 1 March 2016

Revision as of 21:44, 1 March 2016

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:<math> M_{m} =A M_{m-1} - \frac{1}{m-1} (\operatorname{tr}A M_{m-1}) I ~,</math>

and, in comportance with the [[Cayley–Hamilton theorem]],

:<math> \operatorname{adj}(A) =(-)^{n-1} M_{n}=(-)^{n-1} (A^{n-1}+c_{n-1}A^{n-2}+ ...+c_2 A+ c_1 I)=(-)^{n-1} \sum_{k=1}^n c_k A^{k-1}~.</math>