On the Perron-Frobenius Theory of Mv-matrices and equivalent properties to eventually exponentially nonnegative matrices

Main Article Content

Thaniporn Chaysri
Dimitrios Noutsos


Mvmatrix is a matrix of the form A = sI −B, where 0 ≤ ρ(B) ≤ s and B is an eventually nonnegative matrix. In this paper, Mvmatrices concerning the Perron-Frobenius theory are studied. Specifically, sufficient and necessary conditions for an Mvmatrix to have positive left and right eigenvectors corresponding to its eigenvalue with smallest real part without considering or not if index0B 1 are stated and proven. Moreover, analogous conditions for eventually nonnegative matrices or Mvmatrices to have all the non Perron eigenvectors or generalized eigenvectors not being nonnegative are studied. Then, equivalent properties of eventually exponentially nonnegative matrices and Mvmatrices are presented.  Various numerical examples are given to support our theoretical findings.

Article Details