3
votes
2answers
264 views

Eigenvectors and eigenvalues of Tridiagonal matrix with varying diagonal elements

is it possible to analytically evaluate the eigenvectors and the eigenvalues of a tridiagonal $n\times n$ matrix of the form : \begin{pmatrix} 1 & b & 0 & ... & 0 \\\ b & 2 ...
0
votes
1answer
164 views

eigenvalues of two nonnegative matrices

Let $A$ and $B$ be symmetric non-negative matrices. If $A\geq B$ (i.e., $A-B$ is a nonnegative matrix), can we say that $\lambda_i(A) \geq \lambda_i(B)$ for all $i$, where $\lambda_i$ denotes the ...
2
votes
1answer
575 views

Non symmetric matrices with real eigenvalues

Consider the following block matrix $A=\pmatrix{A_1 & A_2\cr kA_2^\top & A_3}$ where $A_1$ is a symmetric matrix, $A_3$ is diagonal matrix and all entries of $A$ are real and non-negative. ...