Inverses of \(M\)-type matrices created with irreducible eventually nonnegative matrices (Q865431)

The paper generalizes a classical result that the inverse of a nonsingular irreducible \(M\)-matrix is positive, where an \(M\)-matrix is one that can be expressed as \(\alpha I -P\) for \(P\) entry-wise nonnegative. The generalization is to matrices of the form \(\alpha I -P\) with \(P\) an irreducible eventually nonnegative matrix for which the multiplicity of zero as a root of the minimal polynomial of \(P\) does not exceed one.