P†-matrices: a generalization of P-matrices

Abstract

For , let r(A,B) (c(A,B)) be the set of matrices whose rows, (columns) are independent convex combinations of the rows (columns) of . Johnson and Tsatsomeros have shown that the set r(A,B) (c(A,B)) consists entirely of nonsingular matrices if and only if is a -matrix. For , let . Rohn has shown that if all the matrices in are invertible, then , and are -matrices. In this article, we define a new class of matrices called -matrices and present certain extensions of the above results to the singular case, where the usual inverse is replaced by the Moore–Penrose generalized inverse. The case of the group inverse is briefly discussed.