I'm currently obsessed with the identity det $\det (I \mathbf{I} - At)^{-1} \mathbf{A}t)^{-1} = \exp tr \text{tr } \log (I \mathbf{I} - At)^{-1}. \mathbf{A}t)^{-1}$. It's straightforward to prove algebraically, but its combinatorial meaning is very interesting.
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I'm currently obsessed with the identity det (I - At)^{-1} = exp tr log (I - At)^{-1}. It's straightforward to prove algebraically, but its combinatorial meaning is very interesting. |
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