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The nature and non- negative matrix norm of random matrices

Author: GaoYing
Tutor: RenFangGuo
School: Shaanxi Normal University
Course: Basic mathematics
Keywords: Non-negative Matrix Nonnegative irreducible matrix Idempotent matrix Random matrix Doubly stochastic matrix Matrix norm
CLC: O151.21
Type: Master's thesis
Year: 2011
Downloads: 91
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Abstract


This paper studies the non- negative matrix , nonnegative irreducible matrices related properties , explores the norm of random matrices and the conjugated similar to occupy an important role in the ( ? ) Related to the nature of paper is divided into four chapters, based on knowledge of the nature of non- negative matrix , the norm of random matrices , two important issues for discussion , the following are described in detail : In the first chapter , we introduce the notation used in this article , the basic definitions and are used in the text the theorem introduces non- negative matrix , irreducible matrix , random matrix concepts such as on non- negative matrix , irreducible matrix spectral properties and other related theorems in the second chapter , starting from the basics through known definitions, theorems further explore and adopt other methods to construct a new matrix irreducible matrix related properties were summarized , followed with special forms of non- negative nature of idempotent matrices do some research in the third chapter, introduces the random matrix norm the related properties were introduced random matrix 1 - norm 2 - norm and p- norm bounded reached when necessary and sufficient conditions in Chapter 4, section I introduces the matrix ( ? ??) related to the nature of ; the second part introduces linear transformation argumentation AX-XB = C solution of the situation and gives an application .

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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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