Unitarily invariant norm inequalities for matrix means
نویسندگان
چکیده
منابع مشابه
Inequalities for Unitarily Invariant Norms and Bilinear Matrix Products
We give several criteria that are equivalent to the basic singular value majorization inequality (1.1) that is common to both the usual and Hadamard products. We then use these criteria to give a uniied proof of the basic majorization inequality for both products. Finally, we introduce natural generalizations of the usual and Hadamard products and show that although these generalizations do not...
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This paper aims to present some inequalities for unitarily invariant norms. In section 2, we give a refinement of the Cauchy-Schwarz inequality for matrices. In section 3, we obtain an improvement for the result of Bhatia and Kittaneh [Linear Algebra Appl. 308 (2000) 203-211]. In section 4, we establish an improved Heinz inequality for the Hilbert-Schmidt norm. Finally, we present an inequality...
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Let complex matrices $A$ and $B$ have the same sizes. Using the singular value decomposition, we characterize the $g$-inverse $B^{(1)}$ of $B$ such that the distance between a given $g$-inverse of $A$ and the set of all $g$-inverses of the matrix $B$ reaches minimum under the unitarily invariant norm. With this result, we derive additive and multiplicative perturbation bounds of the nearest per...
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A fundamental result of von Neumann’s identifies unitarily invariant matrix norms as symmetric gauge functions of the singular values. Identifying the subdifferential of such a norm is important in matrix approximation algorithms, and in studying the geometry of the corresponding unit ball. We show how to reduce many convex-analytic questions of this kind to questions about the underlying gauge...
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ژورنال
عنوان ژورنال: The Journal of Analysis
سال: 2021
ISSN: 0971-3611,2367-2501
DOI: 10.1007/s41478-020-00286-2