Skip to main content

All Questions

Filter by
Sorted by
Tagged with
4 votes
1 answer
147 views

prove spectral equivalence bounds for inverse fractional power of matrices

The question is an extention to the answered question prove spectral equivalence bounds for fractional power of matrices. Let $A, D \in \mathbb{R}^{n \times n}$ be two symmetric,positive definite and ...
3 votes
1 answer
80 views

prove spectral equivalence bounds for fractional power of matrices

Let $A, D \in \mathbb{R}^{n \times n}$ be two symmetric,positive definite and tri-diagonal matrices for that we know that they are spectrally equivalent, thus ist holds $$ c^- x^\top D x \le x^\top A ...
1 vote
1 answer
88 views

Are these $L_2$-spectral radii approximations strictly increasing?

Suppose that $V$ is a finite dimensional complex Hilbert space. Let $L(V)$ denote the collection of all linear mappings from $V$ to $V$. Let $A_1,\dots,A_r:V\rightarrow V$ be linear operators. Then ...
2 votes
3 answers
216 views

Equivalence of operators

let $T$ and $S$ be positive definite (thus self-adjoint) operators on a Hilbert space. I am wondering whether we have equivalence of operators $$ c(T+S) \le \sqrt{T^2+S^2} \le C(T+S)$$ for some ...
6 votes
1 answer
487 views

Intuitive proof of Golden-Thompson inequality

Sutter et al. [1] in their paper "Multivariate Trace Inequalities" give an intuitive proof of the following Golden-Thompson inequality: For any hermitian matrices $A,B$: $$ \text{tr}(\exp{(A+B)}) \...
6 votes
0 answers
587 views

Lower bound on the sum of singular values for a sum of Hermitian matrices

Denote the eigenvalues of an $n\times n$ matrix $\mathbf{X}$ by $\lambda_i(\mathbf{X})$ and its singular values by $\sigma_i(\mathbf{X})$, $i=1,\ldots,n$. When $\mathbf{X}$ is Hermitian, we know that $...
0 votes
1 answer
72 views

Characterisation of a matrix ordering property

Let $n$ be a positive integer; we consider all matrices mentioned henceforth to be $n$-by-$n$ matrices. Let $A$ and $B$ be matrices wherein all entries are nonnegative (such matrices will be called ...