Results 11 to 20 of about 13,431 (178)
Matrix inequalities for unitarily invariant norms [PDF]
ScienceAsia, 2018 Let Mn be the space of n × n complex matrices. Let λ j(A), j = 1,2, . . . , n, be the eigenvalues of A ∈ Mn repeated according to multiplicity, and |λ(A)| := (|λ1(A)|, |λ2(A)|, . . . , |λn(A)|) with |λ1(A)| 3⁄4 |λ2(A)| 3⁄4 · · · 3⁄4 |λn(A)|.
Jianguo Zhao
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Positivity of Partitioned Hermitian Matrices with Unitarily Invariant Norms [PDF]
Positivity, 2014 We give a short proof of a recent result of Drury on the positivity of a $3\times 3$ matrix of the form $(\|R_i^*R_j\|_{\rm tr})_{1 \le i, j \le 3}$ for any rectangular complex (or real) matrices $R_1, R_2, R_3$ so that the multiplication $R_i^*R_j$ is ...
Li, Chi-Kwong, Zhang, Fuzhen
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Some inequalities for unitarily invariant norms of matrices [PDF]
Journal of Inequalities and Applications, 2011 This article aims to discuss inequalities involving unitarily invariant norms. We obtain a refinement of the inequality shown by Zhan. Meanwhile, we give an improvement of the inequality presented by Bhatia and Kittaneh for the Hilbert-Schmidt norm ...
Wang Shaoheng, Zou Limin, Jiang Youyi
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Local Lidskii's theorems for unitarily invariant norms [PDF]
Linear Algebra and its Applications, 2018 arXiv admin note: text overlap with arXiv:1610 ...
P. Massey, Noelia B. Rios, D. Stojanoff
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Non-commutative Clarkson inequalities for unitarily invariant norms [PDF]
Pacific Journal of Mathematics, 2002 The authors obtain two types of norm inequalities which are extensions of the classical Clarkson inequalities for the Schatten \(p\)-norms in [\textit{C. A. McCarthy}, Isr. J. Math. 5, 249--271 (1967; Zbl 0156.37902)]. The authors show these inequalities by using operator convex and concave functions.
Hirzallah, Omar, Kittaneh, Fuad
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Randomized Subspace Iteration: Analysis of Canonical Angles and Unitarily Invariant Norms [PDF]
SIAM Journal on Matrix Analysis and Applications, 2018 This paper is concerned with the analysis of the randomized subspace iteration for the computation of low-rank approximations. We present three different kinds of bounds.
A. Saibaba
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SYMMETRIC GAUGE FUNCTIONS AND UNITARILY INVARIANT NORMS
The Quarterly Journal of Mathematics, 1960 L. Mirsky
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Convex maps on $\protect \mathbb{R}^n$ and positive definite matrices
Comptes Rendus. Mathématique, 2020 We obtain several convexity statements involving positive definite matrices. In particular, if $A,B,X,Y$ are invertible matrices and $A,B$ are positive, we show that the map \[ (s,t) \mapsto \mathrm{Tr}\,\log \left(X^*A^sX + Y^*B^tY\right) \] is jointly ...
Bourin, Jean-Christophe, Shao, Jingjing
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Interpolating between the arithmetic-geometric mean and Cauchy-Schwarz matrix norm inequalities [PDF]
, 2015 We prove an inequality for unitarily invariant norms that interpolates between the Arithmetic-Geometric Mean inequality and the Cauchy-Schwarz inequality.Comment: 7 pages; v2: corrected a mistake in the proof of Theorem
Audenaert, Koenraad
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Unitarily invariant norm inequalities for matrix means [PDF]
The Journal of Analysis, 2021 AbstractThe main target of this article is to present several unitarily invariant norm inequalities which are refinements of arithmetic-geometric mean, Heinz and Cauchy-Schwartz inequalities by convexity of some special functions.
Zuo, Hongliang, Jiang, Fazhen
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