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::<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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:<math> \operatorname{adj}(A) =(-)^{n-1} M_{n}=(-)^{n-1} (A^{n-1}+c_{n-1}A^{n-2}+ ...+c_2 A+ c_1 I)=(-)^{n-1} \sum_{k=1}^n c_k A^{k-1}~.</math>
==An equivalent but distinct expression==
A compact determinant of an {{mvar|m}}×{{mvar|m}}-matrix solution for the above Jacobi's formula may alternatively determine the coefficients {{mvar|c}},<ref>Brown, Lowell S. (1994). ''Quantum Field Theory'', Cambridge University Press. ISBN 978-0-521-46946-3, p. 54; Also see, Curtright, T. L. and Fairlie, D. B. (2012). "A Galileon Primer", arXiv:1212.6972 , section 3.</ref>▼
▲A compact determinant of an {{mvar|m}}×{{mvar|m}}-matrix solution for the above Jacobi's formula may alternatively determine the coefficients {{mvar|c}}<ref>Brown, Lowell S. (1994). ''Quantum Field Theory'', Cambridge University Press. ISBN 978-0-521-46946-3, p. 54; Also see, Curtright, T. L. and Fairlie, D. B. (2012). "A Galileon Primer", arXiv:1212.6972 , section 3.</ref>
:<math>c_{n-m} = \frac{(-1)^m}{m!}
\begin{vmatrix} \operatorname{tr}A & m-1 &0&\cdots\\
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