Abstract/Details

## Sign patterns of generalized inverses of M-matrix

Chen, Yonghong.   University of Connecticut ProQuest Dissertations Publishing,  1994. 9513868.

### Abstract (summary)

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.

### Indexing (details)

Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences
Title
Sign patterns of generalized inverses of M-matrix
Author
Chen, Yonghong
Number of pages
75
Degree date
1994
School code
0056
Source
DAI-B 55/12, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
979-8-209-05792-5
Neumann, Michael
University/institution
University of Connecticut
University location
United States -- Connecticut
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
9513868
ProQuest document ID
304098072