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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