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Further relationships between certain partial orders of matrices and their squares

✍ Scribed by Jerzy K. Baksalary; Oskar Maria Baksalary; Xiaoji Liu

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 185 KB
Volume: 375
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(03)00605-0

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✦ Synopsis

Theorem 3 of Baksalary and Pukelsheim [Linear Algebra Appl. 151 (1991) 135] asserts that if both A and B are Hermitian nonnegative definite matrices, then the star order A * B between them and the star order A 2 * B 2 between their squares are equivalent and they imply the commutativity property AB = BA. In this paper, relationships between the three conditions mentioned above are reinvestigated in situations where the assumptions on A and B are completely or partially relaxed. Some results concerning the star order are obtained as corollaries to corresponding results referring to the left-star and right-star orders introduced by Baksalary and Mitra [Linear Algebra Appl. 149 (1991) 73].

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