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ALGEBRA AND MATRIX NORMED SPACES
"... Abstract. We begin by looking at why operator spaces are necessary in the study of operator algebras and many examples of and ways to construct operator algebras. Then we examine how certain algebraic relationships, for example the well known relationship Mn(A) ∼ = HomA(A (n)), break down when nor ..."
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norms are placed on them. This leads to ways to correct these ideas using matrixnorms.
A NonInduced Interval Matrix Norm∗
, 2013
"... Farhadsefat, Rohn and Lotfi defined the concept of an induced interval matrix norm. They then raised the question of finding an interval matrix norm which is not induced by any point matrix norm. We introduce such a norm in this paper. ..."
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Farhadsefat, Rohn and Lotfi defined the concept of an induced interval matrix norm. They then raised the question of finding an interval matrix norm which is not induced by any point matrix norm. We introduce such a norm in this paper.
AN ADDITIVE FUNCTIONAL INEQUALITY IN MATRIX NORMED SPACES
, 2013
"... Abstract. Using the fixed point method and the direct method, we prove the HyersUlam stability of an additive functional inequality in matrix normed spaces. ..."
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Abstract. Using the fixed point method and the direct method, we prove the HyersUlam stability of an additive functional inequality in matrix normed spaces.
Guaranteed minimumrank solutions of linear matrix equations via nuclear norm minimization,”
 SIAM Review,
, 2010
"... Abstract The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and col ..."
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Cited by 562 (20 self)
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Abstract The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding
Experience with a matrix norm estimator
 SIAM J. Sci. Statist. Comput
, 1990
"... Reports available from: And by contacting: ..."
Comparison of matrix norms on bipartite spaces
, 2009
"... Two noncommutative versions of the classical L q (L p) norm on the product matrix algebras Mn ⊗ Mm are compared. The first norm was defined recently by Carlen and Lieb, as a byproduct of their analysis of certain convex functions on matrix spaces. The second norm was defined by Pisier and others us ..."
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Cited by 2 (0 self)
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Two noncommutative versions of the classical L q (L p) norm on the product matrix algebras Mn ⊗ Mm are compared. The first norm was defined recently by Carlen and Lieb, as a byproduct of their analysis of certain convex functions on matrix spaces. The second norm was defined by Pisier and others
Matrix Norms and Rapid Mixing for Spin Systems
, 2007
"... We give a systematic development of the application of matrix norms to rapid mixing in spin systems. We show that rapid mixing of both random update Glauber dynamics and systematic scan Glauber dynamics occurs if any matrix norm of the associated dependency matrix is less than 1. We give improved an ..."
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Cited by 6 (0 self)
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We give a systematic development of the application of matrix norms to rapid mixing in spin systems. We show that rapid mixing of both random update Glauber dynamics and systematic scan Glauber dynamics occurs if any matrix norm of the associated dependency matrix is less than 1. We give improved
Matrix Norms and their Sensitivity to Noise a Computational Study
, 2005
"... Most of the objective (cost) functions in optimization techniques utilize norms especially when dealing with signals, vectors, or matrices. In this work, three norms were studied, namely matrix One norm, Infinity norm, and Frobenius (Euclidean or Two) norm. The effect of noise on these matrix nor ..."
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Most of the objective (cost) functions in optimization techniques utilize norms especially when dealing with signals, vectors, or matrices. In this work, three norms were studied, namely matrix One norm, Infinity norm, and Frobenius (Euclidean or Two) norm. The effect of noise on these matrix
On Sketching Matrix Norms and the Top Singular Vector
"... Sketching is a prominent algorithmic tool for processing large data. In this paper, we study the problem of sketching matrix norms. We consider two sketching models. The first is bilinear sketching, in which there is a distribution over pairs of r × n matrices S and n × s matrices T such that for an ..."
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Cited by 4 (2 self)
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Sketching is a prominent algorithmic tool for processing large data. In this paper, we study the problem of sketching matrix norms. We consider two sketching models. The first is bilinear sketching, in which there is a distribution over pairs of r × n matrices S and n × s matrices
LEMMA OF THE MONTH #4 NO SIMILARITYINVARIANT MATRIX NORM
"... www.nathanieljohnston.com/...nosimilarityinvariantmatrixnorm/ A norm ‖ · ‖ on Mn is said to be weakly unitarilyinvariant if ‖UXU∗ ‖ = ‖X ‖ for all U,X ∈ Mn with U unitary. There are many weakly unitarilyinvariant norms (such as the trace norm, operator norm, Frobenius norm, and numerical rad ..."
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www.nathanieljohnston.com/...nosimilarityinvariantmatrixnorm/ A norm ‖ · ‖ on Mn is said to be weakly unitarilyinvariant if ‖UXU∗ ‖ = ‖X ‖ for all U,X ∈ Mn with U unitary. There are many weakly unitarilyinvariant norms (such as the trace norm, operator norm, Frobenius norm, and numerical
Results 1  10
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2,956