The Perron-Frobenius Theorem revisited

被引：7

作者：

Radjavi, H ^{[1
]}

机构：

[1] Dalhousie Univ, Dept Math Stat & Comp Sci, Halifax, NS B3H 3J5, Canada

来源：

POSITIVITY | 1999年 / 3卷 / 04期

关键词：

indecomposable; fixed vector; matrix semigroup; nonnegative; Perron-Frobenius;

D O I：

10.1023/A:1009766219129

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An extension of the Perron-Frobenius Theorem is presented in the much more general setting of indecomposable semigroups of nonnegative matrices. Many features of the original theorem including the existence of a fixed positive vector, a block-monomial form, and spectral stability properties hold simultaneously for these semigroups. The paper is largely self-contained and the proofs are elementary. The classical theorem and some related results follow as corollaries.

引用

页码：317 / 331

页数：15

共 50 条

[41] The Perron-Frobenius theorem - A proof with the use of Markov chains
Al'pin Yu.A.
Al'pina V.S.
[J]. Journal of Mathematical Sciences, 2009, 157 (5) : 675 - 680
[42] Perron-Frobenius theorem for matrices with some negative entries
Tarazaga, P
Raydan, M
Hurman, A
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 328 (1-3) : 57 - 68
[43] AN APPLICATION OF THE PERRON-FROBENIUS THEOREM TO A DAMAGE MODEL PROBLEM
ALZAID, AA
RAO, CR
SHANBHAG, DN
[J]. SANKHYA-THE INDIAN JOURNAL OF STATISTICS SERIES A, 1986, 48 : 43 - 50
[44] Perron-Frobenius theorem for nonnegative multilinear forms and extensions
Friedland, S.
Gaubert, S.
Han, L.
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2013, 438 (02) : 738 - 749
[45] Extension of the Perron-Frobenius theorem: From linear to homogeneous
De Leenheer, P
Aeyels, D
[J]. PROCEEDINGS OF THE 41ST IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-4, 2002, : 4278 - 4281
[46] Nonlinear extensions of the Perron-Frobenius theorem and the Krein-Rutman theorem
Chang, K. C.
[J]. JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2014, 15 (02) : 433 - 457
[47] SIMPLE PROOF OF PERRON-FROBENIUS THEOREM FOR POSITIVE SYMMETRIC MATRICES
NINIO, F
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1976, 9 (08): : 1281 - 1282
[48] A Perron-Frobenius theorem for positive polynomial operators in Banach lattices
Anh, Bui The
Son, Nguyen Khoa
Thanh, Duong Dang Xuan
[J]. POSITIVITY, 2009, 13 (04) : 709 - 716
[49] Generalized Perron-Frobenius Theorem for Multiple Choice Matrices, and Applications
Avin, Chen
Borokhovich, Michael
Haddad, Yoram
Kantor, Erez
Lotker, Zvi
Parter, Merav
Peleg, David
[J]. PROCEEDINGS OF THE TWENTY-FOURTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS (SODA 2013), 2013, : 478 - 497
[50] A Perron-Frobenius theorem for positive polynomial operators in Banach lattices
Bui The Anh
Nguyen Khoa Son
Duong Dang Xuan Thanh
[J]. Positivity, 2009, 13 : 709 - 716

← 1 2 3 4 5 →