Some singular value inequalities on majorisation for positive semi-definite matrices

Jianguo Zhao ()
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Jianguo Zhao: Yangtze Normal University

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 1, 259-266

Abstract: Abstract In this note, some singular value inequalities on majorisation for positive semi-definite matrices are given. First, the weak log-majorisation of the quantity $$ f(A)g(B)\pm f(B)g(A)$$ f ( A ) g ( B ) ± f ( B ) g ( A ) for certain functions is obtained, where A, $$B\ge 0$$ B ≥ 0 . As a consequence, the weak log-majorisation of the quantity $$A^{p}B^{q}\pm B^{p}A^{q}$$ A p B q ± B p A q for p, $$q>0$$ q > 0 is also obtained. Finally, different estimates for the singular values of the quantity $$A^{p}B^{q}\pm B^{p}A^{q}$$ A p B q ± B p A q are deduced for A, $$B>0$$ B > 0 and $$0

Keywords: Singular value inequalities; Majorisation; Positive semi-definite matrices; Unitarily invariant norms; 15A60; 47A63 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00249-2

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