Results 31 to 40 of about 1,268 (93)
Generalized Induced Norms [PDF]
, 2004 Let ||.|| be a norm on the algebra M_n of all n-by-n matrices over the complex field C. An interesting problem in matrix theory is that "are there two norms ||.||_1 and ||.||_2 on C^n such that ||A||=max{||Ax||_2: ||x||_1=1} for all A in M_n.
C.-K. Li +7 more
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A concise proof to the spectral and nuclear norm bounds through tensor partitions
Open Mathematics, 2019 On estimations of the lower and upper bounds for the spectral and nuclear norm of a tensor, Li established neat bounds for the two norms based on regular tensor partitions, and proposed a conjecture for the same bounds to be hold based on general tensor ...
Kong Xu
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On bounds of matrix eigenvalues [PDF]
Math. Inequal. Appl., 10 (2007), pp. 723--726, 2014 In this paper, we give estimates for both upper and lower bounds of eigenvalues of a simple matrix. The estimates are shaper than the known results.
arxiv +1 more source
, 2013 Motivated with a problem in spectroscopy, Sloane and Harwit conjectured in 1976 what is the minimal Frobenius norm of the inverse of a matrix having all entries from the interval [0, 1].
Drnovšek, Roman
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Some Hermite-Hadamard type integral inequalities for operator AG-preinvex functions
Acta Universitatis Sapientiae: Mathematica, 2016 In this paper, we introduce the concept of operator AG-preinvex functions and prove some Hermite-Hadamard type inequalities for these functions. As application, we obtain some unitarily invariant norm inequalities for operators.
Taghavi Ali +2 more
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A class of normal dilation matrices affirming the Marcus-de Oliveira conjecture [PDF]
arXiv, 2020 In this article, we prove a class of normal dilation matrices affirming the Marcus-de Oliveira conjecture.
arxiv
Numerical radius and zero pattern of matrices [PDF]
, 2007 We give tight upper bounds on the numerical range of square matrices in terms of their Frobenius (Euclidian) norm and a combinatorial parameter similar to the clique number of graphs. Our results imply a concise form of the fundamental theorem of Turan in extremal graph theory.
arxiv +1 more source
Operator inequalities of Jensen type
Topological Algebra and its Applications, 2013 We present some generalized Jensen type operator inequalities involving sequences of self-adjoint operators.
Moslehian M. S., Mićić J., Kian M.
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Positivity of Partitioned Hermitian Matrices with Unitarily Invariant Norms
, 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
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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