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8
votes
2answers
1k views

Eigenvalues of nonnegative integer matrices

Edit I realized that the key piece of information that I need is question 1, and so I'd like to rephrase this post: What are the possible eigenvalues of nonnegative integer matrices? Any answer ...
8
votes
4answers
3k views

Eigenvectors and eigenvalues of Tridiagonal matrix

Hi, is it possible to analytically evaluate the eigenvectors and the eigenvalues of a tridiagonal matrix of the form : $$ \mathcal{T}^{a}_n(p,q) = \begin{pmatrix} 0 & q & 0 & 0 ...
6
votes
2answers
144 views

Is a normal matrix satisfying $A^TA=…$ circulant?

Let $A=\{a_{ij}\}$ be a normal matrix such that $a_{ij}\geq 0$ with equality iff $i=j$. Suppose that $$ A^TA=\begin{pmatrix} a & b & \cdots & b\\ b & a & \ddots & \vdots\\ ...
1
vote
1answer
63 views

Are certain normal matrices circulant? (Part 2)

Let $\mathcal{F}$ denote the family of real normal matrices $A$ such that $ A^TA=\begin{pmatrix} a & b \\ b & \ddots \end{pmatrix}$, for $b>0$. As a user observed in the solution of Part 1 ...
0
votes
1answer
1k views

Properties of eigenvalues of general nonnegative matrices

I am aware, that an answer to this question can be found via Perron-Frobenius theory or something very similar, but unfortunately I am far from being an expert in the field and I am unable to find the ...