# Tagged Questions

The tag has no usage guidance.

2k views

### Can the first non-zero eigenvalue of a Laplacian matrix with more than 1 zero valued eigenvalue be used to reorder an adjacency matrix?

I have a graph with multiple connected components, and its adjacency matrix. I form the Laplacian matrix (wiki Laplacian matrix), and from the 1K nodes there around ...
458 views

### Eigenvalues of permutations of a real matrix: how complex can they be?

This is sort of complementary to this thread. I’ll repeat the definitions here: For a matrix $M\in GL(n,\mathbb R)$, consider the $n!$ matrices obtained by permutations of the rows (say) of $M$ and ...
7k views

Suppose I have the symmetric tridiagonal matrix: $\begin{pmatrix} a & b_{1} & 0 & ... & 0 \\\ b_{1} & a & b_{2} & & ... \\\ 0 & b_{2} & a & ... & 0 \... 1answer 441 views ### Eigenvectors as continuous functions of matrix - diagonal perturbations The general question has been treated here, and the response was negative. My question is about more particular perturbations. The counterexamples given in the previous question have variations not ... 1answer 882 views ### Gaussian kernel eigenfunctions I'm a newbie and may be this question is bit simple for you but pardon me if it's too simple and provide me some references. What is the eigenfunction of a multivariate Gaussian kernel: \begin{... 2answers 379 views ### Does small Perron-Frobenius eigenvalue imply small entries for integral matrices? Suppose that$M$is an$n \times n$matrix where each entry is a positive integer. Then$M$is Perron-Frobenius and so has unique largest real eigenvalue$\lambda_{\textrm{PF}}$. Does an upper ... 1answer 662 views ### Why are 1 and -1 eigenvalues of this matrix? This is a subject I've been working on for a very long time now, but still did not manage to fully understand the interesting properties of this matrix$\mathbf{A}$. First, let's define two matrices: ... 3answers 144 views ### Can a block matrix with at least 3 zero blocks of different size on the diagonal and 1's everywhere else have only integer eigenvalues? Let$M=\begin{pmatrix} \begin{array}{cccccccc} 0 & 0 & 1 & 1 & 1 & 1 & 1 &1\\ 0 & 0 & 1 & 1 & 1 & 1 & 1 &1\\ 1 & 1 & 0 & 0 & ...
I was investigating a problem and came up with the following symmetric tridiagonal matrix (with zero diagonal elements):  \left(\begin{array}{cccccc} 0 & a & 0 & \ldots & 0 \\ a &...
Let $M\in\mathbb{R}^{n\times n}$ be symmetric positive definite and consider a matrix $Q\in\mathbb{R}^{n\times m}$ ($m<n$) with orthonormal columns ($Q^TQ=I$). I'm interested in finding an exact ...