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Let $A$ be an $N\times N$ square matrix. There exists a determinant identity $$\operatorname{det}\left(I+A\right)=1+\sum_m A_{mm}+\frac1{2!}\sum_{m,n}\left| \begin{array}{cc} A_{mm} & A_{mn} \\ A_{nm} & A_{nn}\end{array}\right|+ \frac1{3!}\sum_{m,n,l}\left| \begin{array}{ccc} A_{mm} & A_{mn} & A_{ml} \\ A_{nm} & A_{nn} & A_{nl} \\ A_{lm} & A_{ln} & A_{ll}\end{array}\right|+\ldots$$ Could you please recall me how is this relation usually named?

joriki
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  • Not my area of expertise, but perhaps http://math.stackexchange.com/questions/137951/symmetric-and-exterior-power-of-representation/138794#138794, and http://math.stackexchange.com/questions/142164/determinant-of-a-sum, may be of help. – KR136 Apr 11 '16 at 22:31
  • Neither an expert, but perhaps this? Fredholm determinant – Sangchul Lee Apr 11 '16 at 22:36
  • I am less confident with my previous comment. As far as I know, Fredholm utilized the identity above to derive what is now called Fredholm series expansion of determinant, but I am not clear whether your identity itself is attributed to him or to anyone else... – Sangchul Lee Apr 11 '16 at 23:06

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Jean Dieudonné in his "History of functional analysis" refers to this identity as to von Koch's formula. There a few more references which seem to confirm this naming.

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