Some results on non-negative matrices
Marvin D. Marcus, Henry Minc, B. N. Moyls · Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics · 1961
R ecently Mirsky and F arahat proposed the problem of characterizing the class of doubly stochastic mat riees for which t he least number of permutation matrices necessary to r epresent it as a convex su m has a prescribed va lu e.It is shown that this number can be related t o t he number of eigenvalues of modulus one.The problem of similarity of doubly stochastic matrices is also treated .Finally, the question of t ransitivity of powers of sets of functions on t he first n positive integers into itself is treated by defi ning a corresponding incidence mat rix and exa minin g its powers .