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Consider the $(m+n) \times (m+n)$ block matrix $$M = \begin{bmatrix} A & B \\ C & D \end{bmatrix}$$ I need references where they are talking about the relation between the eigenvalues of $M$ ...

One can show that the following statement holds: Given symmetric matrix $A \in \Re^{n \times n}$ and tall matrix $B \in \Re^{n \times p}$ with full column rank, $$\begin{bmatrix}A & B \\ B^T &...

I am interested in block matrices $A$, that is $A\in M_{n\times n}(R)$ where $R=M_{s\times s}(k)$ and $k$ is a field, such that for every positive integer $m$ the matrix $A^m$ has only scalar blocks ...

Let $A$ be an $n \times n$ real symmetric matrix. Let $$ M = \begin{pmatrix} A & X \\ X^T & A \end{pmatrix} $$ where $X$ is a real invertible $n \times n$ matrix. I am interested in finding ...