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.

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.

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Homework ?

( 2021-07-01 23:44:31 +0100 )edit

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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.

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