【作者】 程静；

【导师】 何承源；

【作者基本信息】 西华大学 ， 应用数学， 2010， 硕士

【摘要】 主要研究两类重要的,具有特殊性质的矩阵——广义酉矩阵和广义Hermite矩阵.关于酉矩阵与Hermite矩阵的研究,目前已经取得了丰富的成果,而随着应用的需要和研究的深入,酉矩阵和Hermite矩阵的各种推广也应运而生.如近年来研究比较多的广义酉矩阵和广义Hermite矩阵,在信息论、线性系统论、经济数学、组合数学、辛几何、控制论等众多学科领域都是十分有用的.本文重点研究广义酉矩阵和广义Hermite矩阵的各种特殊性质,进一步拓广了广义酉矩阵和广义Hermite矩阵的理论体系.主要内容安排如下:第一章前言.第二章广义酉矩阵和广义正交矩阵的特殊性质.第三章广义(斜)Hermite矩阵的特殊性质.第四章k -广义酉矩阵和k -广义Hermite矩阵的性质.更多还原

【Abstract】 This thesis focuses on two kinds of important special matrixes: generalized unitary matrix and generalized Hermite matrix .Study on unitary matrix and Hermite matrix have been received fruitful achievements, with more and more need of application and deep rearching ,various kinds of populurization of unitary matrix and Hermite matrix have been produced . Such as the generalized unitary matrix and the generalized Hermite matrix ,which have been studied more and more in recent years. They are very useful in Information Theory ,Linear System Theory, Business Mathematics, Combinatoral Mathematics, Pungent Geometry, Control Theory and so on. This thesis focuses on studiing the properties of generalized unitary matrix and generalized Hermite matrix.The arrangement of the thesis is shown as following:Chapter 1 mainly introduce the basic definitions of unitary matrix, Hermite matrix, generalized unitary matrix, generalized Hermite matrix and their basic properties.Chapter 2 the generalized unitary matrix’properties and the generalized orthogonal matrix’properties.Chapter 3 the generalized Hermite matrix’properties and the generalized oblique matrix’properties.Chapter 4 the k ? generalized Hermite matrix and thek ? generalized unitary matrix’properties.更多还原