Journal ArticleDOI
Hermitian Matrix Inequalities and a Conjecture
N. N. Chan,Man Kam Kwong +1 more
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This article is published in American Mathematical Monthly.The article was published on 1985-10-01. It has received 43 citations till now. The article focuses on the topics: Symmetric matrix & Matrix function.read more
Citations
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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.
Journal ArticleDOI
REML estimation: asymptotic behavior and related topics
TL;DR: In this paper, the authors show that the restricted maximum likelihood (REML) estimates of dispersion parameters (variance components) in a general (non-normal) mixed model are defined as solutions of the REML equations, and give a necessary and sufficient condition for asymptotic normality of Gaussian maximum likelihood estimates in non-normal cases.
Journal ArticleDOI
Majorizations and inequalities in matrix theory
TL;DR: In matrix theory, majorization plays a significant role as discussed by the authors, and majorization relations among eigenvalues and singular values of matrices produce a lot of norm inequalities and even matrix inequalities.
Asymptotic properties of the empirical blup and blue in mixed linear models
TL;DR: In this paper, the best linear unbiased estimators (BLUE) of fixed effects, with unknown variance components substituted by the REML estimates, are jointly asymptotically normal with the estimates.
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Introduction to Matrix Analysis. By Richard Bellman. 2nd Edition. Pp. xxiii, 403. £7·50. (McGraw-Hill.)
TL;DR: This book discusses Maximization, Minimization, and Motivation, which is concerned with the optimization of Symmetric Matrices, and its applications in Programming and Mathematical Economics.
References
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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
Introduction to Matrix Analysis
TL;DR: In this article, the Second Edition Preface is presented, where Maximization, Minimization, and Motivation are discussed, as well as a method of Hermite and Quadratic Form Index.
Book
Monotone Matrix Functions and Analytic Continuation
TL;DR: In this article, the analysis of Bergman Kernels has been studied in the context of Loewner's Differential Equation and the Spectral Theorem of Pick Functions.
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.