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The Perron-Frobenius Theory and Its Deduction Based on the Wielandt Method

Author: WangZuoZuo
Tutor: LiSiZe
School: Beijing Jiaotong University
Course: Basic mathematics
Keywords: Non-negative irreducible matrix Perron-Frobenius theory Spectral radius Nonnegative irreducible matrix structure of the spectrum
CLC: O151.21
Type: Master's thesis
Year: 2010
Downloads: 36
Quote: 1
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Abstract


Algebraic representation of the rise in the early seventies of the last century, a new branch of algebra , its basic content is the study of the structure of the ring with algebra . This theory has been extraordinarily rapid development in 30 years time and tend to improve . Is square , Perron First discovered in 1907 , some spectral properties , 1908 to 1912 Frobenius expand and promote Perron results to non - negative matrix especially to non-negative irreducible matrix circumstances . In 1973 to 1975 , the case study can about matrix also achieved satisfactory results. For the study of the nature of the matrix spectrum , both in theory actually has its value . In various types of matrix spectral analysis , especially for the Markov chain theory , equations , partial differential equation (s) of the application of the general theory of numerical solution , has been a hot topic for scientists very concerned about . Based on the value of the above results of its application , the article on the spectral properties of the matrix and the structure of a series of research and promotion . This article mainly by introducing non-negative irreducible matrix (including the positive square ) Perron-Frobenius theory , and using Wielandt way to deduce this theory ( a variety of methods to deduce this theory , see [ 5 ] and the literature [ 6 ] ), resulting in general non- negative phalanx Perron-Frobenius theory of classical results and its promotion . Some inference can give estimates of the spectral radius boundaries , as well as analysis of the spectral structure of the non-negative irreducible matrix , this matrix iterative analysis plays an important role , especially in theory .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Theory of algebraic equations,linear algebra > Linear Algebra > Matrix theory
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