# Questions tagged [block-matrices]

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### Eigenvalues and eigenvectors of k-blocks matrix

I'm trying to find the eigenvalues and eigenvectors of the following $n\times n$ matrix, with $k$ blocks. \begin{gather*} X = \left( \begin{array}{cc} A & B & \cdots & \\ B & A & ...
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### Diagonalizing a block tridiagonal matrix

Is there an efficient way to diagonalize a block tridiagonal $N\times N$ matrix of the following form: \begin{matrix} A_0 & B & 0 & 0 & \ldots \\ B & A_1 & B & 0 & \...
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### Solving nonlinear differential multi-variable equation with block-matrices

Here is the problem: Given a formula $f:\mathbb{R}^{n+k}\rightarrow\mathbb{R}^n$, written as $f(x_1(t),x_2(t),...,x_n(t);a1,...ak)$ with $k$ real unknown parameters $a_1,...,a_k$. For any $(a1,...ak)$,...
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### Minimum of $\mathrm{rank}\left( \boldsymbol{W} \boldsymbol{H} \right)$, with $\boldsymbol{W}$ block diagonal

Let us assume that we have a full-rank $(n\cdot l)\times k$ matrix, $\boldsymbol{H}$, with no specific structure (e.g., a realization of a Gaussian i.i.d. random matrix), and an $m\times (n\cdot l)$ ...
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1 vote
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### Eigenvalue distribution of a band matrix

Let $\mathbf M_i$ be rectangular matrices of dimensions $N_{i-1}\times N_i$. We assume that their entries are random, with zero mean and variance $\sigma_i^2$. For some positive integer $k$, I define ...
• 864
1 vote
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### A closed-form expression for the inverse of a block-matrix

Let $\bf A$ be an $n \times n$ non-singular matrix over $\mathbb{F}$. Let $x$ be a non-zero element of $\mathbb{F}$. Suppose that ${\bf 1}_{n}$ is a symbol for the all-one vector of length $n$ ...
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### How to compute a simultaneous block-diagonalization?

Let $n$ be a positive integer and consider of finite set $S \subset M_n(\mathbb{C})$ such that $S^* = S$ (i.e. if $a \in S$ then $a^* \in S$). The algebra generated by $S$ is a finite dimensional $*$-...