Results 11 to 20 of about 10,056 (177)
Isometries for unitarily invariant norms
Linear Algebra and Its Applications, 2005 After a brief survey of results and proof techniques in the study of isometries for unitarily invariant norms on real and complex rectangular matrices, the paper presents a characterization of a class of linear isometries without the linearity assumption.
Jor-Ting Chan +2 more
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Unitarily invariant norms related to the numerical radius
Linear Algebra and Its Applications, 2006 AbstractWe determine the maximum in the class of unitarily invariant norms ∥·∥ such that w(A)⩾∥A∥ for all n-square matrices A. Here w(A) denotes the numerical radius of A.
Ando, T.
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Norms on complex matrices induced by random vectors II: extension of weakly unitarily invariant norms [PDF]
Canadian mathematical bulletin, 2023 We improve and expand in two directions the theory of norms on complex matrices induced by random vectors. We first provide a simple proof of the classification of weakly unitarily invariant norms on the Hermitian matrices. We use this to extend the main
Ángel Chávez +2 more
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A structure theorem for the polars of unitarily invariant norms [PDF]
Proceedings of the American Mathematical Society, 1985 The unitarily invariant norms of matrices, or operators, are essentially the symmetric norms of their singular values. A subclass of these norms depending upon only a few largest of the singular values is considered, and the polars of these norms are characterized. The result is then used to obtain generalizations of some well-known inequalities.
Mudholkar, Govind S., Freimer, Marshall
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Positivity of partitioned Hermitian matrices with unitarily invariant norms [PDF]
Positivity, 2014 6 ...
Li, Chi Kwong, Zhang, Fuzhen
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Submultiplicativity vs subadditivity for unitarily invariant norms
Linear Algebra and its Applications, 2004 The authors prove that if \(A\) and \(B\) are two \(n\)-by-\(n\) nonzero positive semidefinite matrices and \(\|\cdot\|\) is a unitarily invariant norm on matrices satisfying \(\|\text{diag}(1,0,\dots, 0)\|\geq 1\), then the inequalities \[ {\| AB\|\over\| A\|\,\| B\|}\leq {\| A+ B\|\over\| A\|+\| B\|}\quad\text{and}\quad {\| A\circ B\|\over \| A\|\,\|
Hiai, Fumio, Zhan, Xingzhi
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On unitarily invariant norms of matrix-valued linear positive operators
Journal of Inequalities and Applications, 2002 In this paper we prove several inequalities concerning invariant norms of matrices belonging to the range of some matrix-valued Linear Positive Operator (LPO).
Tilli Paolo, Capizzano Stefano Serra
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Some inequalities for unitarily invariant norm
Linear Algebra and its Applications, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Matharu, Jagjit Singh +1 more
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Unification of the arithmetic–geometric mean and Hölder inequalities for unitarily invariant norms
Linear Algebra and Its Applications, 2019 In this paper, we obtain an inequality for unitarily invariant norms which unifies the arithmetic–geometric mean inequality and the Holder inequality for unitarily invariant norms.
Limin Zou
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Volume ratio, sparsity, and minimaxity under unitarily invariant norms [PDF]
2013 IEEE International Symposium on Information Theory, 2013 The current paper presents a novel machinery for studying non-asymptotic minimax estimation of high-dimensional matrices, which yields tight minimax rates for a large collection of loss functions in a variety of problems. Based on the convex geometry of finite-dimensional Banach spaces, we first develop a volume ratio approach for determining minimax ...
Zongming Ma, Yihong Wu 0001
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