Path product matrices

A new class of nonnegative matrices, called the path product (PP) matrices, is introduced. Every inverse M-matrix is PP and this fact gives transparent proofs of a number of facts about inverse M-matrices that hold in a broader setting. For n≤ 3 (and not greater) the (strict) PP matrices are exactly the inverse M-matrices. Finally, the PP matrices are studied, a number of properties given, and the completion problem is solved for partial PP matrices. Unlike other properties inherited by principal submatrices, there is no graphtheoretic restriction on completability of partial PP matrices.