All Questions

Let $G$ be a directed graph and let $P_i$ be its vertices. Let $A$ be the corresponding adjacency matrix of $G$, i.e. $a_{i,j}=1$ if and only if there is a directed edge from $P_i$ to $P_j$, ($a_{i,...

Let $ M \in \mathbb{R}^{n \times n} = \begin{bmatrix} A & B \\ B^T & C \end{bmatrix} $ for some nonnegative $A \in \mathbb{R}^{k \times k}, B \in \mathbb{R}^{k \times n-k}, C \in \mathbb{R}^{n-...

My problem concerns finding a reference in which the formulae for the eigenvalues and the corresponding eigenvectors ($n$ linearly independent eigenvectors!) for the transition matrix of a simple ...

Kindly help me to prove/disprove the following statement. Let $A$ be a symmetric matrix of order $n \times n$ with all the diagonal entry equal to $0$, and other non-diagonal entry equal to $k$ (...