Decomposition of nonnegative group-monotone matrices

Authors:
S. K. Jain, Edward K. Kwak and V. K. Goel

Journal:
Trans. Amer. Math. Soc. **257** (1980), 371-385

MSC:
Primary 15A09; Secondary 15A23, 15A48

DOI:
https://doi.org/10.1090/S0002-9947-1980-0552264-3

MathSciNet review:
552264

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A decomposition of nonnegative matrices with nonnegative group inverses has been obtained. This decomposition provides a new approach to the solution of problems relating to nonnegative matrices with nonnegative group inverses. As a consequence, a number of results are derived. Our results, among other things, answer a question of Berman, extend the theorems of Berman and Plemmons, DeMarr and Flor.

**[1]**A. Ben-Israel and T. N. E. Greville,*Generalized inverses: Theory and applications*, Wiley, New York, 1974. MR**0396607 (53:469)****[2]**A. Berman,*Nonnegative matrices which are equal to their generalized inverse*, Linear Algebra and Appl.**9**(1974), 261-265. MR**0352143 (50:4630)****[3]**A. Berman and R. J. Plemmons,*Matrix group monotonicity*, Proc. Amer. Math. Soc.**46**(1974), 355-359. MR**0352116 (50:4603)****[4]**R. Cline,*Inverses of rank invariant powers of a matrix*, SIAM J. Numer. Anal.**5**(1968), 182-197. MR**37**#2769. MR**0227184 (37:2769)****[5]**R. DeMarr,*Nonnegative idempotent matrices*, Proc. Amer. Math. Soc.**45**(1974), 185-188. MR**0354738 (50:7215)****[6]**P. Flor,*On groups of nonnegative matrices*, Compositio Math.**21**(1969), 376-382. MR**0257115 (41:1769)****[7]**S. K. Jain, V. K. Goel and Edward K. Kwak,*Nonnegative matrices having same nonnegative Moore-Penrose and group inverses*, Linear and Multilinear Algebra**7**(1979), 59-72. MR**523649 (80f:15007)****[8]**R. Penrose,*A generalized inverse for matrices*, Proc. Cambridge Philos. Soc.**51**(1955), 406-413. MR**0069793 (16:1082a)**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
15A09,
15A23,
15A48

Retrieve articles in all journals with MSC: 15A09, 15A23, 15A48

Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1980-0552264-3

Article copyright:
© Copyright 1980
American Mathematical Society