Matrix inequalities with applications to the theory of iterated kernels

Abstract

For an m × n matrix A with nonnegative real entries, Atkinson, Moran and Watterson proved the inequality s(A)3 ≤ mns(AAtA), where At is the transpose of A, and s(·) is the sum of the entries. We extend this result to finite products of the form AAtAAt . . .A or AAtAAt . . .At and give some applications to the theory of iterated kernels.