广义酉矩阵和广义Hermite矩阵性质的推广
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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.
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.
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.
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.
引文
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[3]袁晖坪.关于k-广义酉矩阵[J].数学杂志,2007,(4)
[4]张君敏,吴捷云. k-拟次正交矩阵[J].惠州学院学报,2003,(12)
[5]于江明,谢清明.次Hermite矩阵的次相合与次对角化[J].西南师范大学学报,2003(2)
[6]于江明,谢清明.次正定Hermite矩阵次Schur补的性质[J].数学杂志,2006,(2)
[7]袁晖坪.关于次酉矩阵与次镜像矩阵[J].数学杂志,2002,(3)
[8]袁晖坪.关于次酉矩阵[J].渝州大学学报,1999,(9)
[9]袁晖坪.拟酉矩阵与拟Hermite矩阵[J].数学理论与应用, 2001,(6)
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[11]赵雪.广义酉矩阵性质的拓广[J].北华大学学报(自然科学版),2004,(4)
[12]荣建英,刘绪庆.广义正交矩阵及其性质[J].中国西部科技,2008,(30)
[13]袁晖坪.拟正交变换与拟对合变换[J].渝州大学学报,2001,(3)
[14]袁晖坪.次正交矩阵与次对称矩阵[J].西南师范大学学报,1998,(4)
[15]郭伟.广义次对称矩阵及广义次正交矩阵[J].西南师范大学学报,2000,(1)
[16]郭伟.广义正交基,正交变换及正交矩阵[J].大学数学,2005,(3)
[17]沈光星.广义正定矩阵及其性质[J].高等学校计算数学学报,2002,(2)
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[19]余新良.幂等Hermite矩阵性质探讨[J].湖南工程学院学报,2008,(6)
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[21]罗兵,宋乾坤.次Hermite矩阵方程[J].大学数学,2006,(5)
[22]纪云龙,贾岸平.广义对称矩阵的判定(I)[J].长春工业大学学报,2005,(1)
[23]纪云龙,贾岸平.广义对称矩阵的判定(II)[J].长春工业大学学报,2007,(12)
[24]李范良,胡锡炎.广义中心对称矩阵的结构与性质[J].湖南大学学报,2005,(1)
[25]胡锡炎,张磊.广义次对称矩阵的左右特征值问题[J].计算数学,2007,(4)
[26]贾志刚,王殿军.行(列)对称矩阵的QR分解[J].中国科学A辑,2002,(9)
[27]蔺小林,蒋耀林.酉对称矩阵的QR分解及其算法[J].计算机数学,2005,(5)
[28] VILLEGAS S.A Neumann problem with asymmetric nonlinearity and related minimizing problem [ J ].J Diff Egns,1998,145(1):145-155
[29] SUNJ,LI W.Multiple positive soutions to second order Neumann boundary value problems [ J ].Appl Math Comput,2003,146(2):187-194
[30] LIX JINH D.Optimal existence theory for single and multiple solutions to second order Neumann boundary value poblems[ J ].Indian J Pure and Appl Math,2004,102(1):135-144
[2]袁晖坪.广义酉矩阵与广义Hermite矩阵[J].数学杂志,2003,(3)
[3]袁晖坪.关于k-广义酉矩阵[J].数学杂志,2007,(4)
[4]张君敏,吴捷云. k-拟次正交矩阵[J].惠州学院学报,2003,(12)
[5]于江明,谢清明.次Hermite矩阵的次相合与次对角化[J].西南师范大学学报,2003(2)
[6]于江明,谢清明.次正定Hermite矩阵次Schur补的性质[J].数学杂志,2006,(2)
[7]袁晖坪.关于次酉矩阵与次镜像矩阵[J].数学杂志,2002,(3)
[8]袁晖坪.关于次酉矩阵[J].渝州大学学报,1999,(9)
[9]袁晖坪.拟酉矩阵与拟Hermite矩阵[J].数学理论与应用, 2001,(6)
[10]徐进,盛兴平.广义酉矩阵和广义Hermite矩阵的约当标准形[J].合肥大学学报(自然科学版),2006,(12)
[11]赵雪.广义酉矩阵性质的拓广[J].北华大学学报(自然科学版),2004,(4)
[12]荣建英,刘绪庆.广义正交矩阵及其性质[J].中国西部科技,2008,(30)
[13]袁晖坪.拟正交变换与拟对合变换[J].渝州大学学报,2001,(3)
[14]袁晖坪.次正交矩阵与次对称矩阵[J].西南师范大学学报,1998,(4)
[15]郭伟.广义次对称矩阵及广义次正交矩阵[J].西南师范大学学报,2000,(1)
[16]郭伟.广义正交基,正交变换及正交矩阵[J].大学数学,2005,(3)
[17]沈光星.广义正定矩阵及其性质[J].高等学校计算数学学报,2002,(2)
[18]游兆永,袁超伟.几类广义正定矩阵之间的关系及有关性质[J].工程数学学报,1993,(6)
[19]余新良.幂等Hermite矩阵性质探讨[J].湖南工程学院学报,2008,(6)
[20]侯谦民,刘修生.广义酉矩阵和广义Hermite矩阵的张量积与诱导矩阵[J].数学杂志,2007,(5)
[21]罗兵,宋乾坤.次Hermite矩阵方程[J].大学数学,2006,(5)
[22]纪云龙,贾岸平.广义对称矩阵的判定(I)[J].长春工业大学学报,2005,(1)
[23]纪云龙,贾岸平.广义对称矩阵的判定(II)[J].长春工业大学学报,2007,(12)
[24]李范良,胡锡炎.广义中心对称矩阵的结构与性质[J].湖南大学学报,2005,(1)
[25]胡锡炎,张磊.广义次对称矩阵的左右特征值问题[J].计算数学,2007,(4)
[26]贾志刚,王殿军.行(列)对称矩阵的QR分解[J].中国科学A辑,2002,(9)
[27]蔺小林,蒋耀林.酉对称矩阵的QR分解及其算法[J].计算机数学,2005,(5)
[28] VILLEGAS S.A Neumann problem with asymmetric nonlinearity and related minimizing problem [ J ].J Diff Egns,1998,145(1):145-155
[29] SUNJ,LI W.Multiple positive soutions to second order Neumann boundary value problems [ J ].Appl Math Comput,2003,146(2):187-194
[30] LIX JINH D.Optimal existence theory for single and multiple solutions to second order Neumann boundary value poblems[ J ].Indian J Pure and Appl Math,2004,102(1):135-144