Faddeev–LeVerrier algorithm: Difference between revisions

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The objective is to calculate the coefficients {{math|''c<sub>k</sub>''}} of the characteristic polynomial of the {{math|''n''×''n''}} matrix {{mvar|A}},
::<math>p_A(\lambda)\equiv \det(\lambda I_n-A)=\sum_{k=0}^{n} c_k \lambda^k~,</math>
where, evidently, {{math|''c<sub>n</sub>''}} = 1 and(characteristic polynomials are [[Monic polynomial|monic polynomials]]) and {{math|''c''}}<sub>0</sub> = (−1)<sup>''n''</sup> det {{mvar|A}}.
 
The coefficients {{math|''c<sub>n-i</sub>''}} are determined by induction on {{mvar|i}}, using an auxiliary sequence of matrices
:<math> \begin{align}
M_0 &\equiv 0 & c_n &= 1 \qquad &(k=0) \\