Matrix inequalities with applications to the theory of iterated kernels Original Research Article

For an m×n matrix A with nonnegative real entries, Atkinson, Moran and Watterson proved the inequality s(A)3less-than-or-equals, slantmns(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 AAtAAtcdots, three dots, centeredA or AAtAAtcdots, three dots, centeredAt and give some applications to the theory of iterated kernels.