I wonder if we can express the following term by using "Trace function"? $$(X-\mu)^T \Sigma^{-1}(X-\mu)$$ This is the quadratic term in Multivariate Gaussian Distribution with mean of $\mu$ and covariance matrix of $\Sigma$. I need to know if I can express it by using $Tr()$ function (which is the sum of diagonal in matrix algebra).
Thanks in advance,
Yes, since your expression is scalar-valued, and the trace of a scalar is the scalar itself. $$ \eqalign { (X-\mu)^T\Sigma^{-1}(X-\mu) &= {\rm tr}\big((X-\mu)^T\Sigma^{-1}(X-\mu)\big) \cr &= {\rm tr}(\Sigma^{-1}(X-\mu)(X-\mu)^T) \cr }$$ Where the final line is a result of the cyclic permutation property of the trace.