JOURNAL BROWSE
Search
Advanced SearchSearch Tips
NONNEGATIVE INTEGRAL MATRICES HAVING GENERALIZED INVERSES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
NONNEGATIVE INTEGRAL MATRICES HAVING GENERALIZED INVERSES
Kang, Kyung-Tae; Beasley, LeRoy B.; Encinas, Luis Hernandez; Song, Seok-Zun;
  PDF(new window)
 Abstract
For an nonnegative integral matrix A, a generalized inverse of A is an nonnegative integral matrix G satisfying AGA = A. In this paper, we characterize nonnegative integral matrices having generalized inverses using the structure of nonnegative integral idempotent matrices. We also define a space decomposition of a nonnegative integral matrix, and prove that a nonnegative integral matrix has a generalized inverse if and only if it has a space decomposition. Using this decomposition, we characterize nonnegative integral matrices having reflexive generalized inverses. And we obtain conditions to have various types of generalized inverses.
 Keywords
idempotent matrix;regular matrix;generalized inverse matrix;
 Language
English
 Cited by
 References
1.
R. B. Bapat, Structure of a nonnegative regular matrix and its generalized inverses, Linear Algebra Appl. 268 (1998), 31-39. crossref(new window)

2.
H. H. Cho, Regular fuzzy matrices and fuzzy equations, Fuzzy Sets and Systems 105 (1999), no. 3, 445-451. crossref(new window)

3.
K. H. Kim and F. W. Roush, Inverses of Boolean Matirces, Linear Algebra Appl. 22 (1978), 247-262. crossref(new window)

4.
R. J. Plemmons and R. E. Cline, The generalized inverse of a nonnegative matrix, Proc. Amer. Math. Soc. 39 (1973), 26-32. crossref(new window)

5.
K. M. Prasad, Generalized inverses of matrices over commutative rings, Linear Algebra Appl. 211 (1994), no. 1, 35-52. crossref(new window)

6.
P. S. S. N. V. P. Rao and K. P. S. B. Rao, On generalized inverses of Boolean matrices, Linear Algebra Appl. 1 (1975), no. 2, 135-153.