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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
doaj   +6 more sources

Norm inequalities for functions of matrices [PDF]

Heliyon
In this paper, we prove several spectral norm and unitarily invariant norm inequalities for matrices in which the special cases of our results present some known inequalities. Also, some of our results give interpolating inequalities which are related to
Ahmad Al-Natoor
doaj   +2 more sources

Unitarily invariant norms related to the numerical radius [PDF]

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.
exaly   +3 more sources

Quadratic Forms in Random Matrices with Applications in Spectrum Sensing [PDF]

Entropy
Quadratic forms with random kernel matrices are ubiquitous in applications of multivariate statistics, ranging from signal processing to time series analysis, biomedical systems design, wireless communications performance analysis, and other fields ...
Daniel Gaetano Riviello, Giusi Alfano, Roberto Garello   +2 more
doaj   +2 more sources

Unitarily invariant norm inequalities for matrix means [PDF]

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.
Hongliang Zuo
exaly   +3 more sources

Lower bounds for the low-rank matrix approximation [PDF]

Journal of Inequalities and Applications, 2017
Low-rank matrix recovery is an active topic drawing the attention of many researchers. It addresses the problem of approximating the observed data matrix by an unknown low-rank matrix. Suppose that A is a low-rank matrix approximation of D, where D and A
Jicheng Li, Zisheng Liu, Guo Li
doaj   +2 more sources

Extensions of interpolation between the arithmetic-geometric mean inequality for matrices [PDF]

Journal of Inequalities and Applications, 2017
In this paper, we present some extensions of interpolation between the arithmetic-geometric means inequality. Among other inequalities, it is shown that if A, B, X are n × n $n\times n$ matrices, then ∥ A X B ∗ ∥ 2 ≤ ∥ f 1 ( A ∗ A ) X g 1 ( B ∗ B ) ∥ ∥ f
Mojtaba Bakherad, Rahmatollah Lashkaripour, Monire Hajmohamadi   +2 more
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Some results of Heron mean and Young’s inequalities [PDF]

Journal of Inequalities and Applications, 2018
In this paper, we will show some improvements of Heron mean and the refinements of Young’s inequalities for operators and matrices with a different method based on others’ results.
Changsen Yang, Yonghui Ren
doaj   +2 more sources

Several unitarily invariant norm inequalities for matrices

Annals of Functional Analysis
This paper presents new inequalities involving unitarily invariant norms of matrices, extending classical results such as the Cauchy-Schwarz and arithmetic-geometric mean inequalities in the matrix setting. The authors build upon and generalize recent work by \textit{K. M. R. Audenaert} [Oper. Matrices 9, No.
Junjian Yang
exaly   +3 more sources

Unitarily invariant norms on operators

Acta Scientiarum Mathematicarum, 2022
Let $f$ be a symmetric norm on ${\mathbb R}^n$ and let ${\mathcal B}({\mathcal H})$ be the set of all bounded linear operators on a Hilbert space ${\mathcal H}$ of dimension at least $n$. Define a norm on ${\mathcal B}({\mathcal H})$ by $\|A\|_f = f(s_1(A), \dots, s_n(A))$, where $s_k(A) = \inf\{\|A-X\|: X\in {\mathcal B}({\mathcal H}) \hbox{ has rank ...
Chan, Jor-Ting, Li, Chi-Kwong
openaire   +2 more sources