Faddeev–LeVerrier algorithm: Difference between revisions

Revision as of 12:03, 1 March 2016

Revision as of 13:16, 1 March 2016

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This can be easiest achieved through the following auxiliary equation (Hou, 1998),

::<math>\lambda \frac{\partial p(\lambda) }{ \partial \lambda} -n p =\operatorname{tr} AB~.</math>

This is but the trace of the the defining equation for {{mvar|B}} after multiplying it by dint {{mvar|B}} on the right, andof utilizing [[Jacobi's formula]],

:<math>\frac{\partial p(\lambda)}{\partial \lambda}= p(\lambda) \sum^\infty _{m=0}\lambda ^{-(m+1)} \operatorname{tr}A^m =

p(\lambda) ~ \operatorname{tr} \frac{I}{\lambda I -A}\equiv\operatorname{tr} B~. </math>