数学季刊 ›› 1995, Vol. 10 ›› Issue (2): 59-66.

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Several Inequalities of Matrix Traces

  

  1. Hainan  Normal  College


  • 收稿日期:1994-03-18 出版日期:1995-06-30 发布日期:2025-03-21

Several Inequalities of Matrix Traces


  1. Hainan  Normal  College
  • Received:1994-03-18 Online:1995-06-30 Published:2025-03-21

摘要:  This paper has made the result of generalization and the answer according to the result of question raised in [1].
Especially we cancel the strong factors(A·B=B·A)in Theorerm 4 in [2]. We get the result to the same as the result of the inequality of Cauchy-Schwarz and Holder in the matrix. Finally,the paper also is a refinement of these two inequalities.It inserts the continuous integral value into the inequalities of matrix mean,and it becomes the inequality of integral form of continuous measure.

关键词: inequality, matrix trace, positive definite

Abstract:  This paper has made the result of generalization and the answer according to the result of question raised in [1].
Especially we cancel the strong factors(A·B=B·A)in Theorerm 4 in [2]. We get the result to the same as the result of the inequality of Cauchy-Schwarz and Holder in the matrix. Finally,the paper also is a refinement of these two inequalities.It inserts the continuous integral value into the inequalities of matrix mean,and it becomes the inequality of integral form of continuous measure.

Key words: inequality, matrix trace, positive definite

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