Majorization relations for Hadamard products
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TLDR
The conjecture of Johnson and Bapat on the Hadamard product of positive definite matrices was shown to be false in this paper, and the conjecture was confirmed by the authors of this paper.About:
This article is published in Linear Algebra and its Applications.The article was published on 1995-07-01 and is currently open access. It has received 32 citations till now. The article focuses on the topics: Hadamard matrix & Complex Hadamard matrix.read more
Citations
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Book
Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory
TL;DR: This book brings together a vast body of results on matrix theory for easy reference and immediate application with hundreds of identities, inequalities, and matrix facts stated rigorously and clearly.
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A Surrogate-Assisted Reference Vector Guided Evolutionary Algorithm for Computationally Expensive Many-Objective Optimization
TL;DR: A surrogate-assisted reference vector guided evolutionary algorithm (SAEA) for computationally expensive optimization problems with more than three objectives that uses Kriging to approximate each objective function to reduce the computational cost.
Journal ArticleDOI
A Clustering-Based Adaptive Evolutionary Algorithm for Multiobjective Optimization With Irregular Pareto Fronts
TL;DR: A clustering-based adaptive MOEA that adaptively generate a set of cluster centers for guiding selection at each generation to maintain diversity and accelerate convergence is proposed for solving MOPs with irregular Pareto fronts.
Journal ArticleDOI
A quantitative version of the observation that the Hadamard product is a principal submatrix of the Kronecker product
TL;DR: In this paper, the spectral norm of the Hadamard product of two n×m matrices A and B is shown to be bounded by a constant factor κ(·) for a real non-singular matrix X and invertible diagonal matrices D,E.
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References
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Book
Inequalities: Theory of Majorization and Its Applications
TL;DR: In this paper, Doubly Stochastic Matrices and Schur-Convex Functions are used to represent matrix functions in the context of matrix factorizations, compounds, direct products and M-matrices.
Book
Fundamentals of the Theory of Operator Algebras
TL;DR: In this article, the authors compare normal states and unitary equivalence of von Neumann algebras, including the trace and the trace trace of the trace of a projection.
Journal ArticleDOI
Concavity of certain maps on positive definite matrices and applications to Hadamard products
TL;DR: In this article, the concavity and convexity theorems for tensor products of positive definite matrices were proved for affine positive functions on (0, ∞) matrices.
Book ChapterDOI
Topics in matrix analysis: The Hadamard product
Roger A. Horn,Charles R. Johnson +1 more
Journal ArticleDOI
Log majorization and complementary Golden-Thompson type inequalities
Tsuyoshi Ando,Fumio Hiai +1 more
TL;DR: In this article, a log majorization result for power means of positive semidefinite matrices was obtained, which implies matrix norm inequalities for unitarily invariant norms, which are considered as complementary to the Golden-Thompson one.