Logarithmic convexity of perron-frobenius eigenvectors of positive matrices

Siddhartha Sahi

doi:10.1090/S0002-9939-1993-1139482-5

Logarithmic convexity of perron-frobenius eigenvectors of positive matrices

Siddhartha Sahi

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Let C(S) be the cone of Perron-Frobenius eigenvectors of stochastic matrices that dominate a fixed substochastic matrix S. For each 0 ≤ α ≤ 1, it is shown that if u and v are in C(S) then so is w, where w_j = u^α_jv^1-α_j.

Original language	English (US)
Pages (from-to)	1035-1036
Number of pages	2
Journal	Proceedings of the American Mathematical Society
Volume	118
Issue number	4
DOIs	https://doi.org/10.1090/S0002-9939-1993-1139482-5
State	Published - Aug 1993
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Keywords

Convexity
Perron-Frobenius eigenvector
Positive matrix
Stochastic matrix

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10.1090/S0002-9939-1993-1139482-5

Cite this

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title = "Logarithmic convexity of perron-frobenius eigenvectors of positive matrices",

abstract = "Let C(S) be the cone of Perron-Frobenius eigenvectors of stochastic matrices that dominate a fixed substochastic matrix S. For each 0 ≤ α ≤ 1, it is shown that if u and v are in C(S) then so is w, where wj = uαjv1-αj.",

keywords = "Convexity, Perron-Frobenius eigenvector, Positive matrix, Stochastic matrix",

author = "Siddhartha Sahi",

year = "1993",

month = aug,

doi = "10.1090/S0002-9939-1993-1139482-5",

language = "English (US)",

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T1 - Logarithmic convexity of perron-frobenius eigenvectors of positive matrices

AU - Sahi, Siddhartha

PY - 1993/8

Y1 - 1993/8

N2 - Let C(S) be the cone of Perron-Frobenius eigenvectors of stochastic matrices that dominate a fixed substochastic matrix S. For each 0 ≤ α ≤ 1, it is shown that if u and v are in C(S) then so is w, where wj = uαjv1-αj.

AB - Let C(S) be the cone of Perron-Frobenius eigenvectors of stochastic matrices that dominate a fixed substochastic matrix S. For each 0 ≤ α ≤ 1, it is shown that if u and v are in C(S) then so is w, where wj = uαjv1-αj.

KW - Convexity

KW - Perron-Frobenius eigenvector

KW - Positive matrix

KW - Stochastic matrix

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U2 - 10.1090/S0002-9939-1993-1139482-5

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SP - 1035

EP - 1036

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 4

ER -

Logarithmic convexity of perron-frobenius eigenvectors of positive matrices

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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