In literature, I found the following identity. Unfortunately, I fail to see why this holds. Where does the trace of the matrix come from? Any clarifications are highly appreciated!
2026-03-26 17:30:30.1774546230
Question about trace of matrix
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Trace has the property of $Tr(AB)=Tr(BA)$
\begin{align}\sum_{n=1}^N (x_n-\bar{x})^TC^{-1}(x_n-\bar{x})&=\sum_{n=1}^N Tr((x_n-\bar{x})^TC^{-1}(x_n-\bar{x}))\\ &= \sum_{n=1}^N Tr(C^{-1}(x_n-\bar{x})(x_n-\bar{x})^T)\\ &=Tr(C^{-1}\sum_{n=1}^N (x_n-\bar{x})(x_n-\bar{x})^T)\\\end{align}