Results 151 to 160 of about 19,389 (202)

Unitarily invariant norm inequalities for positive semidefinite matrices

Linear Algebra and its Applications, 2021
Let \(M_n(\mathbb{C})\) denote the space of all \(n\times n\) complex matrices. \textit{F. Kittaneh} [J. Funct. Anal. 250, No. 1, 132--143 (2007; Zbl 1131.47009)] proved that if \(A, B, X \in M_n(\mathbb{C})\) such that \(A, B\) are positive semidefinite, then \[ \|| AX-XB |\| \le \Vert X\Vert~\|| A \oplus B |\|, \] where \(\|| \cdot |\|\) denotes the ...
Ahmad Al-Natoor, Sakina Benzamia, F. Kıttaneh   +2 more
semanticscholar   +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, Shengyan Ma
semanticscholar   +3 more sources

Unitarily Invariant Operator Norms

Canadian Journal of Mathematics, 1983
1.1. Over the past 15 years there has grown up quite an extensive theory of operator norms related to the numerical radius1of a Hilbert space operator T. Among the many interesting developments, we may mention:(a) C. Berger's proof of the “power inequality”2(b) R. Bouldin's result that3for any isometry V commuting with T;(c) the unification by B.
Fong, C.-K., Holbrook, J. A. R.
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Unitarily invariant norm submultiplicativity

Linear and Multilinear Algebra, 1992
In this paper, we view rules for multiplying matrices (such as the Hadamard product, usual product and Kronecker product) as combinatorial objects. Our purpose is to determine conditions on these objects that imply submultiplicativity with respect to the spectral norm and certain of the unitarily invariant norms.
Charles R. Johnson, Peter Nylen
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A Mirsky-Type Unitarily Invariant Norm Inequality for Dual Quaternion Matrices and Its Applications

Symmetry
In this paper, we present a Mirsky-type unitarily invariant norm inequality for dual quaternion matrices, which can be regarded as a singular value perturbation theorem for dual quaternion matrices.
Jing Zhong, Ping Zhong
semanticscholar   +1 more source

Inequalities for Unitarily Invariant Norms

SIAM Journal on Matrix Analysis and Applications, 1998
Let \(A,B,X\) be complex matrices with \(A,B\) positive semidefinite. The author proves the following generalization of the arithmetic-mean inequality due to \textit{R. Bhatia} and \textit{C. Davis} [ibid. 14, No. 1, 132-136 (1993; Zbl 0767.15012]: \[ (2+t)\| A^rXB^{2-r}+A^{2-r}XB^r\| \leq 2\| A^2X+tAXB+XB^2\| \] for arbitrary unitarily invariant norm \
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A note on unitarily invariant matrix norms

Linear Algebra and its Applications, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ding, Wenxuan, Li, Chi-Kwong, Li, Yuqiao
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Unitarily invariant norms on finite von Neumann algebras

Acta Scientiarum Mathematicarum, 2023
The authors generalize the celebrated theorem of \textit{J. von Neumann} [Mitt. Forsch.-Inst. Math. Mech. Univ. Tomsk 1, 286--299 (1937; Zbl 0017.09802)] on unitarily invariant norms on \(n\times n\) matrices to the context of finite von Neumann algebras \(\mathcal{R}\). A norm \(\alpha\) on a unital \(C^*\)-algebra \(\mathcal{A}\) is called normalized
Haihui Fan, Don Hadwin
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Generalized Unitarily Invariant Gauge Regularization for Fast Low-Rank Matrix Recovery

IEEE Transactions on Neural Networks and Learning Systems, 2020
Spectral regularization is a widely used approach for low-rank matrix recovery (LRMR) by regularizing matrix singular values. Most of the existing LRMR solvers iteratively compute the singular values via applying singular value decomposition (SVD) on a ...
Xixi Jia, Xiangchu Feng, Weiwei Wang, Lei Zhang   +3 more
semanticscholar   +1 more source

Interpolating inequalities for unitarily invariant norms of matrices

Advances in Operator Theory
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ahmad Al-Natoor, O. Hirzallah, F. Kıttaneh   +2 more
semanticscholar   +3 more sources