Faddeev–LeVerrier algorithm: Difference between revisions

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:<math>c_{n-m}= -\frac{1}{m}(c_n \mathrm{tr} A^m+c_{n-1} \mathrm{tr} A^{m-1}+...+c_{n-m+1}\mathrm{tr} A)= -\frac{1}{m}\sum_{k=1}^{m} c_{n-m+k} \mathrm{tr} A^k ~ ; ...</math>
 
Observe {{math|''A<sup>−1</sup> {{=}} − M<sub>n</sub> /c<sub>0</sub>'' {{=}} (−1)<sup>''n''−1</sup>''M<sub>n</sub>''/det''A''}} terminates the recursion at {{mvar| λ}}. This could be used to obtain the inverse or the determinant of {{mvar|A}}.
 
==Derivation==