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The Study On Three Generalized Positive Definite Matrices

Posted on:2012-10-12Degree:MasterType:Thesis
Country:ChinaCandidate:W J SunFull Text:PDF
GTID:2120330332990911Subject:Applied Mathematics
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Positive definite matrix got important applications in probability theor y, physics andin all disciplines such as geometry, but with the developme nt of mathematics itself and other disciplines or areas of the matrix (such as input-output matrix theory, mathematical programming, modern control Etc.),more and can not meet the need, so the generalized positive defini te matrix aroused wide attention of scholars at home and abroad and do a lot of important work. In this dissertation, we systematically discuss the generalized positive matrix definition, determination, and received the cor-responding number of conclusions.Chapter One Firstly, The paper introduces the background, application and the research status quo of the Positive definite matrix and then brief ly introduced the main other chapters, finally gives a few definitions and symbol conventions.Chapter Two based on the results of the generalized positive definite matrix PE,we added the distribution of eigenvalues and other supplement.Chapter Three we extended the generalized positive definite matrixPE and expanded to FPE,then we studied its nature, necessary and sufficient c onditions, and added a subset of its unique nature of class.Chapter Four based on the complex positive definite matrix(CP)I,we expanded to(CP)D,then we studies its necessary and sufficient conditions and the nature.In Summary, It is also very important in this paper,we discuss in terms of set theory the relation among real symmetric positive definite matrices---PE,FPE,FPE(E).So that,we not only can more deeply understand the concept of three types of generalized positive definite matrices respectively, and the relationship between them, and also we will have a more clear and thorough understanding. Positive definite matrix of these three comparison become clear relationship between the discussion of this paper.
Keywords/Search Tags:generalized positive definite matrix P_E, generalized positive definite matrix FP_E, complex positive definite matrix(CP)_D, collection class
PDF Full Text Request
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