一个矩阵逆向不等式的推广

数学季刊 ›› 2005, Vol. 20 ›› Issue (1): 21-27.

一个矩阵逆向不等式的推广

Faculty of Science, Xi'an Jiaotong University, Xi'an 710049, China; Department of Mathematics, Beihua University, Jilin 132011, China; Department of Mathematic, Putian University, Putian 351100, China

收稿日期:2003-01-20 出版日期:2005-03-30 发布日期:2024-01-25
作者简介:FENG Xiao-xia(1969-),female,native of Jilin,Jilin,an associate professor of Beihua Univer- sity,a doctored student of Xi'an Jiaotong University,engages in wavelet and matrix analysis;YANG Zhong- peng(1947-),male,native of Jilin,Jilin,a professor of Putian University,engages in the theory of matrix algebra and its application.
基金资助:
Supported by the Science Foundation of Educational Commission of Fujian Province (JA03157) Supported by the Scientific Research Item of Putian University(20042002)；

The Generalization of a Converse of Matrix Inequality

Faculty of Science, Xi'an Jiaotong University, Xi'an 710049, China; Department of Mathematics, Beihua University, Jilin 132011, China; Department of Mathematic, Putian University, Putian 351100, China

Received:2003-01-20 Online:2005-03-30 Published:2024-01-25
About author:FENG Xiao-xia(1969-),female,native of Jilin,Jilin,an associate professor of Beihua Univer- sity,a doctored student of Xi'an Jiaotong University,engages in wavelet and matrix analysis;YANG Zhong- peng(1947-),male,native of Jilin,Jilin,a professor of Putian University,engages in the theory of matrix algebra and its application.
Supported by:
Supported by the Science Foundation of Educational Commission of Fujian Province (JA03157) Supported by the Scientific Research Item of Putian University(20042002)；

摘要/Abstract

摘要： We prove that the inequality ... holds, when a m ×n real matrix X = (x_ij) whose entries are not all equal to 0 satisfies ... . Therefore we not only generalize the results of Horst Alzer [2] from non-negative matrix to real matrix, but also complete a result of E R van Dam [1], which indicated that the best possible upper bound is equal to 1 for real matrix.

关键词: real matrix, trace, inequality, lower , bound

Abstract: We prove that the inequality ... holds, when a m ×n real matrix X = (x_ij) whose entries are not all equal to 0 satisfies ... . Therefore we not only generalize the results of Horst Alzer [2] from non-negative matrix to real matrix, but also complete a result of E R van Dam [1], which indicated that the best possible upper bound is equal to 1 for real matrix.

Key words: real matrix, trace, inequality, lower , bound

中图分类号:

O151.21

冯晓霞, 杨忠鹏. 一个矩阵逆向不等式的推广[J]. 数学季刊, 2005, 20(1): 21-27.

FENG Xiao-xia, YANG Zhong-peng. The Generalization of a Converse of Matrix Inequality[J]. Chinese Quarterly Journal of Mathematics, 2005, 20(1): 21-27.

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