# Tagged Questions

**3**

votes

**2**answers

268 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

**1**answer

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

**1**answer

711 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.
...