Content area
Abstract
Let P be an n x n nonnegative stochastic irreducible matrix. Let $A = I - P$ be the associated M-matrix so that A has nonpositive off-diagonal entries and, by the theory of M-matrices, nonnegative principal minors. In this dissertation we investigate under what conditions the group inverse of A remains an M-matrix. For the special classes of stochastic nonnegative matrices comprising of the periodic and nonperiodic Jacobi matrices and of the alternating circulant matrices we determine necessary and sufficient conditions for the group inverse of A to be an M-matrix. Moreover, we investigate the sign patterns of A using a representation formula due to Hunter. Finally, we consider the sign patterns of other generalized inverses of A.
Details
Title
Sign patterns of generalized inverses of M-matrix
Author
Chen, Yonghong
Year
1994
ISBN
979-8-209-05792-5
Source type
Dissertation or Thesis
Language of publication
English
ProQuest document ID
304098072
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
