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Some matrix inequalities of log-majorization type

Part of: General theory of linear operators Basic linear algebra

Published online by Cambridge University Press:  26 February 2021

Bo-Yan Xi  and
Fuzhen Zhang
Bo-Yan Xi*
Affiliation:
College of Mathematics, Inner Mongolia University for Nationalities, Tongliao, Inner Mongolia Autonomous Region 028043P.R. China e-mail: baoyintu78@imun.edu.cn
Fuzhen Zhang
Affiliation:
Department of Mathematics, Nova Southeastern University, Fort Lauderdale, FL33314, USA e-mail: zhang@nova.edu
*
e-mail: baoyintu78@qq.com
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Abstract

The purpose of this paper is twofold: we present some matrix inequalities of log-majorization type for eigenvalues indexed by a sequence; we then apply our main theorem to generalize and improve the Hua–Marcus’ inequalities. Our results are stronger and more general than the existing ones.

Keywords

EigenvalueHua’s determinant inequalitylog-majorizationmajorization inequality

MSC classification

Primary: 15A42: Inequalities involving eigenvalues and eigenvectors
Secondary: 15A45: Miscellaneous inequalities involving matrices 47A63: Operator inequalities
Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 1 , March 2022 , pp. 95 - 105
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Copyright
© Canadian Mathematical Society 2021

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Footnotes

Xi’s work was partially supported by NNSF of China grant no. 11361038.

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