# Questions tagged [kronecker-product]

The Kronecker product of two matrices $\mathbf{A}_{(K\times L)}=\{a_{kl}\}$ and $\mathbf{B}_{(M\times N)}=\{b_{mn}\}$ which is denoted by $\mathbf{A}\otimes\mathbf{B}$ is defined as $$\mathbf{A}\otimes\mathbf{B}=\mathbf{C}_{(KM\times LN)}=\begin{bmatrix}a_{11}\mathbf{B} &\dots & a_{1L}\mathbf{B}\\\vdots &\ddots&\vdots\\a_{K1}\mathbf{B} &\dots & a_{KL}\mathbf{B}\end{bmatrix}$$

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### Is there a matrix that shift data along side the main diagonal?

I am an electrical engineer and I am trying to write my optimization problem in a more compact form. During my time solving this optimization problem, I reallize that I need to keep shifting and ...
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### Weighted Nearest Kronecker Product

For a given $m n$-length vector $a$, the problem of finding an $m$-length vector $x$ and an $n$-length vector $y$ that minimize $$\lVert a - x \otimes y \rVert^2$$ is known as the Nearest Kronecker ...
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### Matrix valued system of equations with right and left product

Let $J$ be a real valued $2\times 2$ matrix with determinant equal to 1. The eigenvalues of $J$ are complex in general. Let $Q$ be a $2\times 2$ matrix satisfying $$J^T Q J = Q$$ Question: Does there ...
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### Implementing Finite Differences solver for 2D Poisson Equation

I'm trying to solve the 2D Poisson equation: $$\begin{cases} -\Delta u = f & \text{in} \hspace{0.2cm} \Omega=(0,1)^{2} \\ g = u & \text{on} \hspace{0.2cm}\partial \Omega \end{cases}$$ Using ...