Norm bounds for Hadamard products and an arithmetic - geometric mean inequality for unitarily invariant norms
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An arithmetic-geometric mean inequality for unitarily invariant norms and matrices, 2∥A∗XB∥⩽∥AA∗ X+XBB∗∥, is an immediate consequence of a basic inequality for singular values of Hadamard products.About:
This article is published in Linear Algebra and its Applications.The article was published on 1995-07-01 and is currently open access. It has received 21 citations till now. The article focuses on the topics: Hadamard's inequality & Inequality of arithmetic and geometric means.read more
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Positive Definite Matrices
TL;DR: In this paper, the authors present a synthesis of the considerable body of new research into positive definite matrices, which have theoretical and computational uses across a broad spectrum of disciplines, including calculus, electrical engineering, statistics, physics, numerical analysis, quantum information theory and geometry.
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Matrix Analysis : Matrix Monotone Functions, Matrix Means, and Majorization
TL;DR: These lecture notes are largely based on my course at Graduate School of Information Sciences of Tohoku University during April-July of 2009 as mentioned in this paper, and the main topics covered in these notes are matrix/operator monotone and convex functions (the Löwner and Kraus theory), operator means (the so-called Kubo-Ando theory), majorization for eigen/singular values of matrices and its applications to matrix norm inequalities, and means of matrics and related norm inequalities.
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A cauchy-schwarz inequality for operators with applications
Rajendra Bhatia,Chandler Davis +1 more
TL;DR: For any unitarily invariant norm on Hilbert-space operators, it is shown in this article that for all operators A, B, X and positive real numbers r we have ||| |A∗XB| r ||| 2 ⩽ ||||AA ∗X| r||| ||| XBB∗| r|.
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Arithmetic–Geometric Mean and Related Inequalities for Operators
TL;DR: Theorem 4, 5, and 6 of as discussed by the authors were derived from integral expressions of relevant operators and they were shown to be direct consequences of integral expressions for operators and unitarily invariant norms.
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Positive definite functions and operator inequalities
TL;DR: In this paper, the authors construct several examples of positive definite functions and use the positive definite matrices arising from them to derive several inequalities for norms of operators, which are then used to derive the inequalities for norm of operators.
References
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Matrix Analysis
Roger A. Horn,Charles R. Johnson +1 more
TL;DR: In this article, the authors present results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrate their importance in a variety of applications, such as linear algebra and matrix theory.
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Topics in Matrix Analysis
TL;DR: The field of values as discussed by the authors is a generalization of the field of value of matrices and functions, and it includes singular value inequalities, matrix equations and Kronecker products, and Hadamard products.
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Bemerkungen zur Theorie der beschränkten Bilinearformen mit unendlich vielen Veränderlichen.
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Maximum Properties and Inequalities for the Eigenvalues of Completely Continuous Operators.
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More matrix forms of the arithmetic-geometric mean inequality
Rajendra Bhatia,Chandler Davis +1 more
TL;DR: For arbitrary $n \times n$ matrices A, B, X, and for every unitarily invariant norm, it was shown in this paper that for any matrices B, A, X and B, it is possible to show that