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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Spectral order preserving matrices and Muirhead's theorem


Author: Kong Ming Chong
Journal: Trans. Amer. Math. Soc. 200 (1974), 437-444
MSC: Primary 26A87; Secondary 15A45
DOI: https://doi.org/10.1090/S0002-9947-1974-0379780-9
MathSciNet review: 0379780
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Abstract: In this paper, a characterization is given for matrices which preserve the Hardy-Littlewood-Pólya spectral order relation $ \prec $ for $ n$-vectors in $ {R^n}$. With this characterization, a new proof is given for the classical Muirhead theorem and some Muirhead-type inequalities are obtained. Moreover, sufficient conditions are also given for matrices which preserve the Hardy-Littlewood-Pólya weak spectral order relation $ \prec\prec$.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0379780-9
Keywords: Hardy-Littlewood-Pólya spectral orders, spectral equivalency, spectral inequalities, rearrangement inequalities, spectral order preserving matrices, full permutation matrices, Muirhead's theorem
Article copyright: © Copyright 1974 American Mathematical Society