Logarithmic convexity of Perron-Frobenius eigenvectors of positive matrices

Author:
Siddhartha Sahi

Journal:
Proc. Amer. Math. Soc. **118** (1993), 1035-1036

MSC:
Primary 15A48; Secondary 15A51

DOI:
https://doi.org/10.1090/S0002-9939-1993-1139482-5

MathSciNet review:
1139482

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the cone of Perron-Frobenius eigenvectors of stochastic matrices that dominate a fixed substochastic matrix . For each , it is shown that if and are in then so is , where .

**[C]**J. Cohen,*Convexity of the dominant eigenvalue of an essentially nonnegative matrix*, Proc. Amer. Math. Soc.**81**(1981), 657-658. MR**601750 (82a:15016)****[DN]**E. Deutsch and M. Neumann,*On the first and second order derivatives of the Perron vector*, Linear Algebra Appl.**71**(1985), 57-76. MR**813033 (87d:15012)****[EJN]**L. Elsner, C. Johnson, and M. Neumann,*On the effect of the perturbation of a nonnegative matrix on its Perron eigenvector*, Czech. Math. J.**32**(1982), 99-109. MR**646715 (83h:15022)****[F]**S. Friedland,*Convex spectral functions*, Linear and Multilinear Algebra**9**(1981), 299-316. MR**611264 (82d:15014)****[K]**J. Kingman,*A convexity property of positive matrices*, Quart. J. Math.**81**(1961), 283-284. MR**0138632 (25:2075)****[S]**E. Seneta,*Non-negative matrices*, George Allen & Unwin, London, 1973. MR**0389944 (52:10773)****[SY]**S. Sahi and S. Yao,*The non-cooperative equilibria of a trading economy with complete markets and consistent prices*, J. Math. Econ.**18**(1989), 325-346. MR**1018983 (90h:90035)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1993-1139482-5

Keywords:
Positive matrix,
stochastic matrix,
Perron-Frobenius eigenvector,
convexity

Article copyright:
© Copyright 1993
American Mathematical Society