Ken Pledger wrote: >Dieter von Holten wrote: >>.... >>the solution is also a square matrix, same size, which has >>only one 1 in each row and column. i learned recently, that >>this is called stochastic matrix. the solution is also >>symmetric to the diagonal.... > >You can't mean that. It would just make every diagonal entry >1, and give you the identity matrix.
What about an anti-diagonal matrix?
What about a transposition matrix?
What about any permutation matrix of order 2 -- that is, a permutation matrix P such that P^2 = I.
The given condition is equivalent to the requirement that the matrix be a product of pairwise disjoint transpositions.