Vedran Šego
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 Feb 5 awarded Nice Answer Feb 3 comment How to prove that the set of real $n \times n$ PSD matrices of rank $\leq r < n$ and unit trace, is not contractible? @Q.Tom. That's what I meant by "multiplying the orthogonal factor with -1". However, this will not always work (if their determinants have opposite sign and the dimension is even). That's why I added the previous comment. Feb 2 comment How to prove that the set of real $n \times n$ PSD matrices of rank $\leq r < n$ and unit trace, is not contractible? @Q.Tom. Happy to help. Btw, ref. "Note 2", if we multiply the orthogonal factor with $\operatorname{diag}(-1,1,1,\dots,1)$, we might get connectedness there for all dimensions. Just an idea; I didn't look deeper into it. Feb 1 revised How to prove that the set of real $n \times n$ PSD matrices of rank $\leq r < n$ and unit trace, is not contractible? added 142 characters in body Feb 1 answered How to prove that the set of real $n \times n$ PSD matrices of rank $\leq r < n$ and unit trace, is not contractible? Jan 16 answered Singular values of $A$ and eigenvalues of $\left[\begin{smallmatrix} 0 & A \\ A^T & 0 \end{smallmatrix}\right]$. Jan 15 answered Pseudo inverse of matrix: SVD vs $A^{T}(A.A^{T})^{-1}$ Jan 9 comment $n^{th}$ minimum/maximum notation @jbaums Yes, it was a typo. I've fixed it (along with two other typos). Thank you. Jan 9 revised $n^{th}$ minimum/maximum notation Fixed several typos Jan 7 answered Inequalities between powers of PSD Jan 7 answered algebraic equation with trace Jan 6 answered Proving that Matrices with same minimal and characteristic polynomial are similar Jan 6 comment Solving an equation with the form $Ax=b$ If $b_{k+2}-2b_{k+1}+b_k \ne 0$ for any $k \ge 1$, then the system has no solutions. Otherwise, you get $n-2$ equations of the form $0_{1 \times n} x = 0$, which are always true and can be discarded, so your system is reduced to the one defined by the first two rows of $A$ and $b$ (2 equations, $n$ unknowns). Jan 6 answered When is the symmetric part of a matrix positive definite? Dec 20 comment summation of determinants of $3\times3$ matrices @Kryštof Exactly. You can write it in the matrix notation, though: $f(X) = XP$, where $P = \left[\begin{smallmatrix} 0 & 1 \\ 1 & 0 \\ & & 1 \end{smallmatrix} \right]$, and then just use the formula $\det(AB) = \det(A)\det(B)$ which, in this case, yields $\det(f(X)) = \det(XP) = \det(X)\det(P) = -\det X$. Dec 20 revised summation of determinants of $3\times3$ matrices added 2 characters in body Dec 20 answered summation of determinants of $3\times3$ matrices Dec 20 comment summation of determinants of $3\times3$ matrices Are you looking for the sum of matrices or the sum of their determinants? Dec 14 answered Show that A,B are similar matrices in S, where S is the set of 2x2 matrices whose square is the zero matrix Nov 23 awarded Revival