## Spectral radius of the product of a right stochastic matrix and a block diagonal matrix

Let us define the following matrix: $C=AB$ where $B$ is a block diagonal matrix with $N$ blocks, $B_1$, $B_2$ … $B_N$, each of dimensions $M \times M$. I know that $B_k = I_M – \mu R_k$ with $R_k$ equals to a hermitian matrix and $\mu$ some positive constant. Moreover, I know that the the entries … Read more

## How to find eigenvalues of following block matrices?

Is there a procedure to find the eigenvalues of A? ‎ A=[XI0I0PPt0II0PPt0⋱⋱⋱⋱⋱0II0PPt0I0k×y−kI00y−k×kYy×y] (All rows and columns except the last are k×k blocks.) where A is adjacency matrix of cubic graphs and X,P are circulant matrices of order k, Y is a matrix of order y, k≠y and I is a identity matrix and 0 is … Read more

## The normalizer of block diagonal matrices

Let G=Un or GLn(C) and H the subgroup of block diagonal matrices respecting a partition n=n1+⋯+nk. Is the normalizer N=NG(H) computed anywhere in the literature? I guess, but haven’t proved, that it is generated by H and the permutations (“transpositions”) exchanging the partition’s same-length segments (ni=nj, if any). I also suspect this may be discussed … Read more

## Is there a formula for the determinant of a block matrix of this kind?

I am looking for an expression that gives the determinant of a matrix of the form \begin{bmatrix} A & B & 0 & \dots & 0 & C \\ B & A & B & & 0 & 0 \\ 0 & B & A & \ddots & 0 & \vdots \\ 0 & & … Read more