Faddeev–LeVerrier algorithm: Difference between revisions

Revision as of 17:03, 29 February 2016

Revision as of 17:09, 29 February 2016

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Thus,

:<math>

M_1= I ~, \quad c_{n-1} = - \mathrm{tr} A ; \qquad M_2= A-I\mathrm{tr} A , \quad c_2c_{n-2}=-\frac{1}{2}\Bigl(\mathrm{tr} A^2 -(\mathrm{tr} A)^2\Bigr) ; \qquad
</math>
<math>M_3= A^2-A\mathrm{tr} A -\frac{1}{2}\Bigl(\mathrm{tr} A^2 -(\mathrm{tr} A)^2\Bigr) I, \quadqquad 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);\quad~\cdots

</math> etc.

etc. Observe {{math|''A⁻¹ {{=}} − M_n /c₀'' {{=}} (−)^''n''−1''M_n''/det''A''}} as the recursion terminates at {{mvar| λ}}.

==Derivation==