Abstract
This paper uses matrix monotone functions as a key tool to obtain several relations among the singular values of certain celebrated matrix quantities. This includes, but is not limited to, relations among the blocks of a block matrix, relations about the singular values of the matrix Heinz means, and some related matrix combinations. Our results improve some celebrated results from the literature.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availibility
Not applicable.
References
Audeh, W.: Singular value inequalities and applications. Positivity 25, 843–852 (2021)
Audeh, W., Kittaneh, F.: Singular value inequalities for compact operators. Linear Algebra Appl. 437, 2516–2522 (2012)
Audenaert, K.: A singular value inequality for Heinz means. Linear Algebra Appl. 422, 279–283 (2007)
Bhatia, R.: Matrix Analysis. Springer, New York (1997)
Bhatia, R.: Positive definite matrices. Princeton University Press, New Jersey (2007)
Bhatia, R., Grover, P.: Norm inequalities related to the matrix geometric mean. Linear Algebra Appl. 437(2), 726–733 (2012)
Bhatia, R., Kittaneh, F.: Notes on matrix arithmetic-geometric mean inequalities. Linear Algebra Appl. 308, 203–211 (2000)
Bourin, J.-C., Lee, E.-Y.: Unitary orbits of Hermitian operators with convex and concave functions. Bull. London Math. Soc. 44, 1085–1102 (2012)
Bourin, J.-C., Lee, E.-Y., Lin, M.: On a decomposition lemma for positive semidefinite block-matrices. Linear Algebra Appl. 437, 1906–1912 (2012)
Dragomir, S.S.: Hermite-Hadamard’s type inequalities for operator convex functions. Appl. Math. Comput. 218(3), 766–772 (2011)
Kittaneh, F.: Notes on some inequalities for Hilbert space operators. Publ. Res. Inst. Math. Sci. 24(2), 283–293 (1988)
Lin, M., Wolkowicz, H.: Hiroshima’s theorem and matrix norm inequalities. Acta Sci. Math. 81, 45–53 (2015)
Sababheh, M.: Convexity and matrix means. Linear Algebra Appl. 506, 588–602 (2016)
Tao, Y.: More results on singular value inequalities. Linear Algebra Appl. 416, 724–729 (2006)
Zhan, X.: Some research problems on the Hadamard product and singular values of matrices. Linear Multilinear Algebra. 47, 191–194 (2000)
Funding
Not applicable.
Author information
Authors and Affiliations
Contributions
The authors (H. R. M) and (M. S.) wrote and validated the results. The author (W. A.) revised the manuscript and added some remarks.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Moradi, H.R., Audeh, W. & Sababheh, M. Singular values inequalities via matrix monotone functions. Anal.Math.Phys. 13, 71 (2023). https://doi.org/10.1007/s13324-023-00832-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s13324-023-00832-8