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应用数学和力学 2024年第9期45卷 1200-1211页

作者： LI Zhen Beijing Institute of Mathematical Sciences and Applications Beijing 101400P.R.China

Real and complex Schur forms have been receiving increasing attention from the fluid mechanics community recently,especially related to vortices and *** decompositions of the velocity gradient tensor,such as the triple decomposition of motion(TDM)and normal-nilpotent decomposition(NND),have been proposed to analyze the local motions of fluid ***,due to the existence of different types and non-uniqueness of Schur forms,as well as various possible definitions of NNDs,confusion has spread widely and is harming the *** work aims to clean up this *** this end,the complex and real Schur forms are derived constructively from the very basics,with special consideration for their *** of uniqueness are *** a general discussion of normality and nilpotency,a complex NND and several real NNDs as well as normal-nonnormal decompositions are constructed,with a brief comparison of complex and real *** on that,several confusing points are clarified,such as the distinction between NND and TDM,and the intrinsic gap between complex and real ***,the author proposes to extend the real block Schur form and its corresponding NNDs for the complex eigenvalue case to the real eigenvalue *** their justification is left to further investigations.

关键词： Schur form normal matrix nilpotent matrix tensor decomposition vortex identification

On Zero One Symmetric and normal Matrices

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Journal of Mathematical Research and Exposition 1998年第2期18卷 159-164页

作者：王伯英张福振北京师范大学数学系美国NovaSoutheastern大学数学科学系

We present additional equivalent conditions on the existence of a 0 1 symmetric matrix with given row sum vector. The case of a 0 1 normal matrix is also considered.

关键词： incidence matrix majorization normal matrix row sum vector.

A new digital approach to design multivariable robust optimal control systems

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2005年第7期6卷 707-710页

作者：刘翔陈琳孙优贤 National Laboratory of Industrial Control Technology Zhejiang University

This paper presents a new design of robust optimal controller for multivariable system. The row characteristic functions of a linear multivariable system and dynamic decoupling of its equivalent system, were applied to change the transfer function matrix of a closed-loop system into a normal function matrix, so that robust H^∞ optimal stability is guaranteed. Furthermore, for the decoupled equivalent control system the I^∞ optimization approach is used to have the closed-loop system embody optimal time domain indexes. A successful application on a heater control system verified the excellence of the new control scheme.

关键词： I^∞/H^∞ Dynamic decoupling normal matrix Row characteristic function

A Note of Spirallike Mappings in C^n

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Chinese Quarterly Journal of Mathematics 1999年第1期14卷 52-54,页

作者：李小申洛阳工学院河南洛阳 471 0 00

In this paper,the Growth and covering Theorems for a kind of spirallike mapping are given.

关键词： spirallike mappings Growth Theorems normal matrix

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矩阵Frobenius范数不等式

高等学校计算数学学报 2009年第1期31卷 42-49页

作者：杨兴东邵保刚吴亚娟南京信息工程大学数理学院

1引言与引理矩阵范数与矩阵奇异值问题是数值代数的重要课题,并在矩阵扰动分析,数值计算等分支中起着重要作用.国内外学者对此已作了大量研究.如关于矩阵特征值扰动界的研究,Hoffman-Wieland获得如下经典结果[2]:

关键词： Probenius norm majorization normal matrix Hermitian matrix

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几个矩阵范数不等式及其在谱扰动中的应用

高等学校计算数学学报 2001年第2期23卷 162-170页

作者：吕火同兴南京航空航天大学理学院南京210016

Inequalities that compare norms of A-B and those of AQ-QB and Q -1 A-BQ -1 and A-QBQ -1 are given, where A and B are either Hermitian or normal matrices and Q is a positive definite matrix. Using these inequalities we... 详细信息

关键词： norm inequality normal matrix perturbation theorem eigenvalue.

ONTHEPROPERTIESOFZCIRCULANTMATRICES

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Transactions of Tianjin University 1996年第1期2卷 91-93页

作者： DING Xueren  WANG Peili (Dept. of Mathematics)

Some properties of Z circulant matrices are given.

关键词： Z circulant matrix normal matrix square matric function

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正规矩阵的任意扰动

高等学校计算数学学报 2000年第1期22卷 85-89页

作者：吕炯兴南京航空航天大学理学院!南京210016

In this paper, we discuss the perturbation of the eigenvalues of a normal matrix. Some results on the perturbation of the eigenvalues of a normal matrix A affected by an arbitrary perturbation A+X are given.

关键词： normal matrix arbitrary perturbations eigenvalue norm.