Ask Your Question
0

Consider the set of all symmetric matrices of a given size $n$ with entries lying in $\{0,1\}$ such that all diagonal entries are zeros in the matrices.

asked 2021-07-01 20:02:46 +0200

anonymous user

Anonymous

updated 2021-07-01 20:04:08 +0200

Consider the set of all symmetric matrices of a given size $n$ with entries lying in {0,1} such that all diagonal entries are zeros in the matrices. Now how to write an algorithm that finds at least one matrix (from the set we have considered) which is similar to its inverse matrix via a permutation matrix.

For computation part, we can choose $n$ according to our convenience.

Please help regarding this. Thank you

edit retag flag offensive close merge delete

Comments

Homework ?

Emmanuel Charpentier gravatar imageEmmanuel Charpentier ( 2021-07-01 23:44:31 +0200 )edit

1 Answer

Sort by ยป oldest newest most voted
0

answered 2021-07-01 23:52:06 +0200

FabianG gravatar image

For even $n = 2k$, you can take a permutation matrix belonging to $k$ disjoint transpositions like $(12)(34)\ldots(n-1,n)$. This is self-inverse, so in particular similar to its inverse.

edit flag offensive delete link more

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

1 follower

Stats

Asked: 2021-07-01 20:02:46 +0200

Seen: 61 times

Last updated: Jul 01