Generalized power symmetric

stochastic matrices

Authors:
R. B. Bapat, S. K. Jain and K. Manjunatha Prasad

Journal:
Proc. Amer. Math. Soc. **127** (1999), 1987-1994

MSC (1991):
Primary 05B20, 15A09, 15A51

DOI:
https://doi.org/10.1090/S0002-9939-99-05126-6

Published electronically:
March 17, 1999

MathSciNet review:
1641629

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Abstract | References | Similar Articles | Additional Information

Abstract: We characterize stochastic matrices which satisfy the equation where are positive integers.

**1.**A. Ben-Israel and T.N.E. Greville,*Generalized Matrix Inverses: Theory and Applications*, Wiley, NY, 1973. MR**53:469****2.**A. Berman and R.J. Plemmons,*Nonnegative Matrices in the Mathematical Sciences*, 2nd edition, SIAM, 1995. MR**95e:15013****3.**S. L. Campbell and C.D. Meyer, Jr.,*Generalized Inverses of Linear Transformations*, Pitman, 1979. MR**80d:15003****4.**S. K. Jain, V.K. Goel and Edward K. Kwak, Nonnegative mth roots of nonnegative O-symmetric idempotent matrices,*Linear Algebra Appl.*23:37-51 (1979). MR**80m:15002****5.**Richard Sinkhorn, Power symmetric stochastic matrices,*Linear Algebra Appl.*40:225-228 (1981). MR**82j:15017**

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Additional Information

**R. B. Bapat**

Affiliation:
Department of Mathematics, Indian Statistical Institute, 7 S.J.S. Sansanwal Marg, New Delhi 110016, India

Email:
rbb@isidl.isid.ac.in

**S. K. Jain**

Affiliation:
Department of Mathematics, Ohio University, Athens, Ohio 45701

Email:
jain@math.ohiou.edu

**K. Manjunatha Prasad**

Affiliation:
Department of Mathematics, Manipal Institute of Technology, Gangtok, Sikkim, 737102 India

DOI:
https://doi.org/10.1090/S0002-9939-99-05126-6

Received by editor(s):
October 22, 1997

Published electronically:
March 17, 1999

Additional Notes:
This work was done while the second author was visiting Indian Statistical Institute in November-December 1996 and July-August 1997. He would like to express his thanks for the warm hospitality he enjoyed during his visits as always. Partially supported by Research Challenge Fund, Ohio University

Communicated by:
Jeffry N. Kahn

Article copyright:
© Copyright 1999
American Mathematical Society