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- W2006880984 abstract "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 A2⩽∗B2 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]." @default.
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- W2006880984 date "2003-12-01" @default.
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- W2006880984 title "Further relationships between certain partial orders of matrices and their squares" @default.
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- W2006880984 doi "https://doi.org/10.1016/s0024-3795(03)00605-0" @default.
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