RE: [math-fun] periodic (-1,0,1) matrices

Wouter wrote: << of the pseudo-anti-symmetric type (sum of anti-symmetric and diagonal). . . . . . . Funny property: only the even n give some matrices with all-zero diagonals, the odd n don't.

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Here's a proof that the odd n can't: Let M' := transpose of M. If M is an n-dim anti-symmetric (i.e., skew-symmetric) matrix for odd n, then det(M) = det(M') = det(-M) = (-1)^n det(M) = -det(M), so det(M) = 0, and so M can't be periodic. --Dan