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About half Hermite positive definite matrix inequality

Author: LianYaoHua
Tutor: YangJin
School: Taiyuan University of Technology
Course: Mathematics and Applied Mathematics
Keywords: Hermite Matrix Semidefinite Track Hadamard product Inequality
CLC: O151.21
Type: Master's thesis
Year: 2011
Downloads: 86
Quote: 0
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Abstract


In recent years , with its own development and its practical mathematical problems , driven semi- positive definite matrix, the matrix of research has become an important issue in the field . Currently, about half Definite Hermite Matrix is a very active research topic . This study is positive semi-definite trace of matrix and its Hermite Some Inequalities Hadamard product , the main contents are as follows: First, we present a brief introduction on the positive semi-definite domestic and foreign research status Hermite matrix and gives some important concepts and some symbols Description ; Secondly, in reference to some scholars on the positive semi-definite Hermite matrix Trace inequality , based on the general and special paper to take a combination of methods to obtain a series of semi- definite Hermite matrix Trace inequality , these theorems have been further from the n semi- definite Hermite matrix Trace Holder and Minkowski inequalities ; Third , we note some positive definite Hermite Matrix Theorem applied to semi- definite Hermite matrix , but Hermite positive definite matrix Hadamard Inequality not apply to semi- definite Hermite matrix view of this, we introduce the Moore-Penrose inverse instead of the general inverse, on this basis, gives some information about positive semi-definite Hermite matrix Hadamard Inequality .

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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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