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TRACE INEQUALITIES FOR MATRICES

Part of: Basic linear algebra

Published online by Cambridge University Press:  02 August 2012

KHALID SHEBRAWI  and
HUSSIEN ALBADAWI
KHALID SHEBRAWI*
Affiliation:
Department of Mathematics, Faculty of Science, Al-Balqa’ Applied University, Salt, Jordan Department of Mathematics, Faculty of Science, Qassim University, Qassim, Saudi Arabia (email: shebrawi@gmail.com)
HUSSIEN ALBADAWI
Affiliation:
Preparatory Year Deanship, King Faisal University, Ahsaa, Saudi Arabia (email: halbadawi@kfu.edu.sa)
*
✉For correspondence; e-mail: shebrawi@gmail.com
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Abstract

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Trace inequalities for sums and products of matrices are presented. Relations between the given inequalities and earlier results are discussed. Among other inequalities, it is shown that if A and B are positive semidefinite matrices then for any positive integer k.

Keywords

trace inequalitieseigenvaluessingular values

MSC classification

Secondary: 15A18: Eigenvalues, singular values, and eigenvectors 15A45: Miscellaneous inequalities involving matrices
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 1 , February 2013 , pp. 139 - 148
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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