OK, here is what is probably a stupid question. Let $M$ be a non-symmetric real matrix: for example, the shear matrix $\left( \begin{array}{cc} 1 & 1 \\ 0 & 1 \end{array} …

Let $A$ and $B$ square real matrices. I know that the matrix $A+B$ has 1 as eigenvalue of multiplicity 1 and the others eigenvalues have their modulus <1. Can we say something a …

Some colleagues and I were wondering if there is a citation out there which shows there are no exceptional eigenvalues, $\lambda$, of classical weight 1/2 Maass forms on $\Gamma_0( …

I have a weighted Laplacian matrix $L$ of a strongly connected directed graph and a diagonal matrix $D$ with positive entries. Since the graph is directed, $L$ is non-symmetric rea …

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 100 eigenvalues …

Let $A$ a $nxn$, non-symmetric, real, Normal matrix with pairs of complex conjugate eigenvalues (and at least one real eigenvalue). I find, through Maple for any $n>2$, that the ma …

Is there any analytic expression for summation of eigen-values of a tri-diagonal matrix which are smaller than a constant value? Or even a rough approximation for it. How about cas …

Suppose we are multiplying matrix $A$ with a diagonal matrix $D$ from left, i.e., $X=D A$ where $D$ is a diagonal matrix with elements $$d_{ii}=\frac{1}{2} \text{ for } i=1,n$$ …

Hello! There are two definitions of graph spectrum: 1) Eigenvalues of adjacency matrix $A$. 2) Eigenvalues of Laplacian of adjacency matrix ($L$). Different sources offer differen …

How to calculate entropy using the eigenvalues when the eigenvalues are negative? http://mathoverflow.net/questions/102569/is-there-a-simple-relation-between-the-entropy-of-a-mat …

Possible Duplicates: Eigenvalues of non-symmetric matrix and its transpose Eigenvalues of the sum of two matrices Hello, I would like to know if there is some relation b …

Is there a procedure to find the eigenvalues of $\textbf{M}$? ‎ $$\begin{eqnarray} ‎\textbf{M}=\left[‎ ‎\begin {array}{ccccc}‎ ‎\textbf{A} & \textbf{B} & & …