A converse of a matrix inequality Original Research Article

We prove: if (xij) is an m×n matrix with non-negative real entries, which are not all equal to 0, thenwith the best possible lower boundOur theorem complements a result of E.R. van Dam [Linear Algebra Appl. 280 (1998) 163], who established that in the case of real entries the best possible upper bound is equal to 1.