All Questions
Tagged with orthogonal-matrices permutations
4 questions
3
votes
1
answer
275
views
Is the Cayley distance on permutation (matrices) equivalent to the Riemannian metric on $O(n)$?
Denote by $d_C(\sigma,\mu)$ the minimal number of transpositions needed to go from a permutation $\sigma$ to a permutation $\mu$. E.g. if $d_C(\sigma,\mu)=0$, then $\sigma=\mu$, if $d_C(\sigma,\mu)=1$,...
- 131
2
votes
2
answers
664
views
On $XX'=I$ such that $AX=XB$ is true when $A,B\in\{0,1\}^{n\times n}$
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 ...
- 13.9k
2
votes
1
answer
3k
views
Number of 5x5 matrix permutations without repetitions in rows or columns
Context
In the boardgame Azul, your goal is to complete as much as possible of a $5\times5$ board by placing 25 tiles of 5 different colours (5 tiles of each colour) so that no colour appears twice in ...
- 123
1
vote
0
answers
238
views
Construct a permutation matrix from some eigenvectors and eigenvalues
Given $n$ orthonormal vectors $v_1, \dots, v_n \in \mathbb R^d$, where $d > n$, we can show that there are many orthogonal matrices $X$ of size $d$ such that $v_1, \dots, v_n$ are eigenvectors of $...
- 111