1.A permutation matrix p is a 0,1-matrix having exactly
one 1 in each row and column.Prove that a square matrix
of nonnegative integers can be expressed as the sum of k
permutation matrices if and only if all row sums and
column sums equal k.
2.A doubly stochastic matrix Q is a nonnegative real matrix
in which every row and every column sums to 1.Prove that
a doubly stochastic matrix Q can be expressed
Q=C1P1+C2P2+....,where C1,C2... are nonnegative real numbers
summing to 1 and P1,P2.... are permutation matrices.
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