More Matrix Forms of the Arithmetic-Geometric Mean Inequality

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Previous article Next article More Matrix Forms of the Arithmetic-Geometric Mean InequalityRajendra Bhatia and Chandler DavisRajendra Bhatia and Chandler Davishttps://doi.org/10.1137/0614012PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractFor arbitrary $n \times n$ matrices A, B, X, and for every unitarily invariant norm, it is proved that $2|||A^ * XB|||\leqq |||AA^ * X + XBB^ * |||$.[1] T. Ando, Concavity of certain maps on positive definite matrices and applications to Hadamard products, Linear Algebra Appl., 26 (1979), 203–241 10.1016/0024-3795(79)90179-4 80f:15023 0495.15018 CrossrefISIGoogle Scholar[2] Rajendra Bhatia, Perturbation bounds for matrix eigenvalues, Pitman Research Notes in Mathematics Series, Vol. 162, Longman Scientific & Technical, Harlow, 1987viii+129 88k:15020 0696.15013 Google Scholar[3] Rajendra Bhatia and , Fuad Kittaneh, On the singular values of a product of operators, SIAM J. Matrix Anal. Appl., 11 (1990), 272–277 10.1137/0611018 90m:47033 0704.47014 LinkISIGoogle Scholar[4] Chandler Davis, An extremal problem for extensions of a sesquilinear form, Linear Algebra and Appl., 13 (1976), 91–102 10.1016/0024-3795(76)90046-X 52:15068 0326.15012 CrossrefISIGoogle Scholar[5] Chandler Davis, , W. M. Kahan and , H. F. Weinberger, Norm-preserving dilations and their applications to optimal error bounds, SIAM J. Numer. Anal., 19 (1982), 445–469 10.1137/0719029 84b:47010 0491.47003 LinkISIGoogle Scholar[6] A. McIntosh, Heinz inequalities and perturbation of spectral families, Macquarie Mathematics Reports, 79-0006, 1979 Google Scholar[7] Colin J. Thompson, Inequality with applications in statistical mechanics, J. Mathematical Phys., 6 (1965), 1812–1813 32:7110 CrossrefISIGoogle ScholarKeywordsgeometric meansingular valuesunitarily invariant norm Previous article Next article FiguresRelatedReferencesCited ByDetails Norm and numerical radius of single operators through tools and techniques from multivariable operator theoryLinear Algebra and its Applications, Vol. 649 | 1 Sep 2022 Cross Ref Refinement of seminorm and numerical radius inequalities of semi-Hilbertian space operatorsMathematica Slovaca, Vol. 72, No. 4 | 9 August 2022 Cross Ref A Hilbert-Schmidt norm Inequality for positive semidefinite matrices related to a question of BourinPositivity, Vol. 26, No. 3 | 27 June 2022 Cross Ref Sharp Bounds for a Generalized Logarithmic Operator Mean and Heinz Operator Mean by Weighted Ones of Classical Operator OnesMathematics, Vol. 10, No. 10 | 10 May 2022 Cross Ref Norm inequalities for positive semidefinite matrices and a question of Bourin IIIPositivity, Vol. 26, No. 1 | 23 February 2022 Cross 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| 1 Apr 1993 Cross Ref Volume 14, Issue 1| 1993SIAM Journal on Matrix Analysis and Applications1-316 History Submitted:11 April 1990Accepted:09 May 1991Published online:17 July 2006 InformationCopyright © 1993 Society for Industrial and Applied MathematicsKeywordsgeometric meansingular valuesunitarily invariant normMSC codes15A4215A6047A3047B0547B10PDF Download Article & Publication DataArticle DOI:10.1137/0614012Article page range:pp. 132-136ISSN (print):0895-4798ISSN (online):1095-7162Publisher:Society for Industrial and Applied Mathematics