Inverses of M-type Matrices Created with Irreducible Eventually Nonnegative Matrices
نویسندگان
چکیده
An M-matrix is a matrix that can be expressed as αI − P, where P is entry wise nonnegative and α ≥ ρ(P ). It is well known that the inverse of a nonsingular irreducible M-matrix is positive. In this paper, matrices of the form αI − P, where P is an irreducible eventually nonnegative matrix and α > ρ(P ), are studied. It is shown that if index0(P ) ≤ 1, then there exists a positive number λ such that if λ > α > ρ(P ), then the inverse of αI − P is positive.
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