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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(\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 {{math|''c''}}<sub>0</sub> = (−)<sup>''n''</sup> det {{mvar|A}}.
The coefficients are determined recursively from the top down, by dint of the auxiliary matrices {{mvar|M}},
:<math> \begin{align}
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