Chinese Quarterly Journal of Mathematics ›› 2005, Vol. 20 ›› Issue (1): 21-27.

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The Generalization of a Converse of Matrix Inequality

  

  1. 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);

Abstract: We prove that the inequality ... holds, when a m ×n real matrix X = (xij) 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

CLC Number: