All Questions

Given real symmetric matrices $A,B\in\{0,1\}^{n\times n}$ is it true that $$AX=XB$$ has a solution of form $X$ a permutation matrix iff a solution with $XX'=I$ exists? We are over reals. It is clear ...

I have a two matrices $A$ and $B$ in $\mathbb{R}^{m \times n }$ ($m \gg $ n) such that there exists an orthonormal matrix $X \in \mathbb{R}^{n \times n }$, such that: $$AX = B$$ Given that $X$ is ...

There are three known $n\times1$ vectors: $a, b, c$, along with one unknown $n\times n$ matrix: $X$. I am only interested in the $n={2,3}$ cases. $X$ is $2\times 2$ or $3\times 3$ rotation matrix ...