All Questions
7 questions
0
votes
1
answer
226
views
Faulty algorithm for simultaneous diagonalization?
I found a simple algorithm for simultaneous diagonalization of two commuting matrices (Nordgren - Simultaneous Diagonalization and SVD of Commuting Matrices), which seemed to be well-founded. For ...
- 103
3
votes
1
answer
182
views
The proof of the invertibility of $\Big( \sin\frac{8kl\pi}{2n+1} \Big)_{k,l=1}^\frac{n}{2}$
Suppose that $n$ is even. Any suggestion/appraoch to prove that $S=\Big( \sin\frac{8kl\pi}{2n+1} \Big)_{k,l=1}^\frac{n}{2}$ is invertible?
- 4,058
2
votes
1
answer
141
views
On the eigen vectors of a diagonalizable matrix
Let us consider the space $M_n(\mathbb{C})$. By a unitary matrix $U=(u_{ij})$ we mean that $U^{-1}=(\overline{u_{ji}})$.
Q. Let $U$ be a unitary matrix. I am looking for the pairs of matrices $(D,A)$ ...
- 4,058
5
votes
1
answer
571
views
Can I assign the term "is eigenvector" and "is eigenmatrix" of matrix $P$ in my specific (infinite-size) case?
Remark: I asked this in MSE, the question got views and votes but seemingly no one had an answer so far.
Background: I'm rereading a couple of my exploratory (surely not research-level) math-essays ...
- 5,342
2
votes
1
answer
508
views
Jordan decomposition of a block matrix
Assume $A$ is a block matrix of the form:
$$A=\left[\begin{array}{cccc}
A_{11}&A_{12}&\ldots&A_{1n}\\
A_{21}&A_{22}&\ldots&A_{2n}\\
\vdots&\vdots&\ddots&\vdots\\
...
- 21
1
vote
1
answer
193
views
Is there any relation between weights in the eigenvector (corresponding to least eigenvalue) and the columns of a correlation matrix?
This problem is motivated from one of my pattern mining research projects. Any helpful suggestions will be highly appreciated.
Consider an $n \times n$ correlation matrix A such that all the off-...
- 141
1
vote
1
answer
136
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Any generic way to move a psd matrix to its neighbors?
Given a two positive matrices $A,B$. For simplicity, let's assume that $Tr A=Tr B=1$. Assume that $\|A-B\|_1\leq\varepsilon$, for some small $\varepsilon>0$, where $\|\cdot\|_1$ is the $l_1$-norm, ...
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