All Questions
Tagged with traces eigenvalues
6 questions
5
votes
1
answer
241
views
Trace inequality under consideration of definiteness
Let $G \in \mathbb{R}^{3 \times 3}$ a symmetric, but indefinite matrix and $U \in \mathbb{R}^{3\times 3}$ a symmetric and positive definite matrix. I would like to prove the inequality
$$ \text{Tr} \...
4
votes
2
answers
3k
views
Maximizing trace of $\mathrm V^T \mathrm A \mathrm V$ for $\mathrm A$ symmetric (alternate proof with min/max-theorem)
I'm trying to work out a proof for the following proposition:
Let $A \in \mathbb{R}^{n,n}$ a real, symmetric matrix with eigenvalues $\lambda_1 \ge \lambda_2 \ge \cdots \ge \lambda_n$, then
$$\max \...
3
votes
1
answer
814
views
Trace and exterior product
Let $V$ be a $2n$-dimensional complex vector space with base $\{e_1,\dotsc,e_n,f_1,\dotsc,f_n]\}$ Let $W \subset \wedge^n V$ be the subspace in the exterior product,
with basis vectors
$$
e_{i_1} \...
2
votes
1
answer
1k
views
Trace inequality for matrices with determinant 1
Let $A$ and $B$ be two matrices with $\det(A)=\det(B)=1$. Does it follow that
$\sqrt{\mathrm{tr}(A^TB^TBA-I)}\le\sqrt{\mathrm{tr}(A^TA-I)}+\sqrt{\mathrm{tr}(B^TB-I)}$
I suspect that this can be ...
1
vote
0
answers
511
views
How to show that the trace of a regularized Laplacian defined on two sphere with radius $h\geq 1$ is diverging logarithmically?
Let $h,m\in[1,\infty)$. I would like to verify that the following sum diverges logarithmically
\begin{equation}
\sum_{d=0}^{\infty} \frac{2d+1}{2h^2(1+\frac{d(d+1)}{h^2})(1+\frac{d(d+1)}{h^2m ^2})^{2}}...
-2
votes
1
answer
262
views
Proving 2 matrices have the same trace [closed]
I found a problem in my textbook and I have tried solving it, but I had no succes. The problem is:
Let $A$ and $B$ be $n \times n$ matrices with complex number entries. Given that $AB−BA$ is ...