An inequality for non-negative matrices Original Research Article

Let A be an n × n matrix with non-negative entries and no entry in (0, 1). We prove that there exist integers r, s with 0 less-than-or-equals, slant r less-than-or-equals, slant s less-than-or-equals, slant 2n such that Ar less-than-or-equals, slant As. We prove that 2n cannot be replaced with e√n log n. We also give an application to the theory of formal languages.