All Questions
2
questions
8
votes
0
answers
713
views
Bounding sum of first singular values squared for Kronecker sum of traceless matrices
Let $A$ and $B$ be $4\times4$ traceless matrices with Hilbert-Schmidt norms summing up to $1/4$, i.e.
$$\text{Tr}\left[ A\right]=\text{Tr}\left[ B\right] = 0,\qquad\text{Tr}\left[ A^\dagger A + B^\...
- 1,592
2
votes
2
answers
185
views
Prove spectral equivalence of matrices
Let $A,D \in \mathbb{R}^{n\times n}$ be two positive definite matrices given by
$$
D =
\begin{bmatrix}
1 & -1 & 0 & 0 & \dots & 0\\
-1 & 2 & -1 & 0 & \dots & 0\\...
- 31