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Suppose we have a set of rank deficient covariance matrices. How can I know the similarities and differences between those set of matrices? Regards,

Given $n$ orthonormal vectors $v_1, \dots, v_n \in \mathbb R^d$, where $d > n$, we can show that there are many orthogonal matrices $X$ of size $d$ such that $v_1, \dots, v_n$ are eigenvectors of $...