Faddeev–LeVerrier algorithm: Difference between revisions

Revision as of 18:51, 29 February 2016

Revision as of 18:57, 29 February 2016

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<math>M_3= A^2-A\mathrm{tr} A -\frac{1}{2}\Bigl(\mathrm{tr} A^2 -(\mathrm{tr} A)^2\Bigr) I, \qquad c_{n-3}=- \tfrac{1}{6}\Bigl( (\operatorname{tr}A)^3-3\operatorname{tr}(A^2)(\operatorname{tr}A)+2\operatorname{tr}(A^3)\Bigr); \qquad \cdots </math> etc.

Observe {{math|''A⁻¹ {{=}} − M_n /c₀'' {{=}} (−)^''n''−1''M_n''/det''A''}} asterminates the recursion terminates at {{mvar| λ}}. This could be used to obtain the inverse or the determinant of {{mvar|A}}.

==Derivation==