自反矩阵在圆盘上的左右逆特征对问题

数学物理学报 ›› 2014, Vol. 34 ›› Issue (6): 1542-1553.

自反矩阵在圆盘上的左右逆特征对问题

李定武¹|刘巍^1,2|沈金荣¹|熊慧军¹

1.长沙学院数学与计算机科学系长沙 410022;
2.湖南大学数学与计量经济学院长沙 410012

收稿日期:2013-05-03 修回日期:2014-07-12 出版日期:2014-12-25 发布日期:2014-12-25

Left and Right Inverse Eigenpairs Problem on Disk of Reflexive Matrices

LI Ding-Wu¹, LIU Wei^1,2, SHEN Jin-Rong¹, XIONG Hui-Jun¹

1.Department of Mathematics and Information Science, Changsha University, Changsha 410022;
2.College of Mathematics and Econometrics, Hunan University, Changsha 410012

Received:2013-05-03 Revised:2014-07-12 Online:2014-12-25 Published:2014-12-25

摘要/Abstract

摘要：

研究了自反矩阵在给定的圆盘上的左右逆特征对问题及其最佳逼近问题, 得到了在特定条件下左右逆特征对问题的一般解及最佳逼近问题的表达式.

关键词: 左右逆特征对, 圆盘, 自反矩阵, Frobenius范数

Abstract:

In this paper, the left and right inverse eigenpairs problem and associated approximation problem on the given disk of
eigenvalues of reflexive matrices are studied. Under special conditions, the general solutions of the left and right inverse
eigenpairs problem are presented, and the expression of the solution for the optimal approximation problem is obtained.

Key words: Left and right inverse eigenvalue, Disk, Reflexive matrix, Frobenius norm

中图分类号:

15A29

李定武, 刘巍, 沈金荣, 熊慧军. 自反矩阵在圆盘上的左右逆特征对问题[J]. 数学物理学报, 2014, 34(6): 1542-1553.

LI Ding-Wu, LIU Wei, SHEN Jin-Rong, XIONG Hui-Jun. Left and Right Inverse Eigenpairs Problem on Disk of Reflexive Matrices[J]. Acta mathematica scientia,Series A, 2014, 34(6): 1542-1553.

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