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4 | typo | ||
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I have not seen precisely this identity before, but it seems to be a variation on Chapman's identity [R. Chapman, Amer. Math. Monthly 109(7) (2002), 664–666], see also arXiv:math/0612464, $\sum_{x_1,x_2,\ldots x_N=0}^{1}(-1)^{x_1+x_2+\cdots x_N} \;\text{det}\;(x_1 A_1+x_2 A_2 +\cdots x_N A_N)=0,$ valid for any set $A_1,A_2,\ldots A_N$ of $d\times d$ matrices, with $N\geq d$d+1$. |
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3 |
mistake
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2 | N >= d | ||
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I have not seen precisely this identity before, but it seems to be a variation on Chapman's identity [R. Chapman, Amer. Math. Monthly 109(7) (2002), 664–666], see also arXiv:math/0612464, $\sum_{x_1,x_2,\ldots x_d=0}^{1}(-1)^{x_1+x_2+\cdots x_dx_N=0}^{1}(-1)^{x_1+x_2+\cdots x_N} \;\text{det}\;(x_1 A_1+x_2 A_2 +\cdots x_d A_d)=0$x_N A_N)=0,$ valid for any set $A_1,A_2,\ldots A_d$ A_N$ of $d\times d$ matrices, with $N\geq d$. |
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