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Generalized power symmetric stochastic matrices

Author(s): R. B. Bapat; S. K. Jain; K. Manjunatha Prasad
Journal: Proc. Amer. Math. Soc. 127 (1999), 1987-1994.
MSC (1991): Primary 05B20, 15A09, 15A51
Posted: March 17, 1999
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Abstract: We characterize stochastic matrices $A$ which satisfy the equation $(A^p) ^T = A^m$ where $p < m$ are positive integers.

References:

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A. Ben-Israel and T.N.E. Greville, Generalized Matrix Inverses: Theory and Applications, Wiley, NY, 1973. MR 53:469

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A. Berman and R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, 2nd edition, SIAM, 1995. MR 95e:15013

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S. L. Campbell and C.D. Meyer, Jr., Generalized Inverses of Linear Transformations, Pitman, 1979. MR 80d:15003

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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

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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: 10.1090/S0002-9939-99-05126-6
PII: S 0002-9939(99)05126-6
Received by editor(s): October 22, 1997
Posted: 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
Copyright of article: Copyright 1999, American Mathematical Society

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