Antieigenvalue techniques in statistics
type: Item
instance of: scholarly article
title: Antieigenvalue techniques in statistics
zbMATH Open document ID: 1168.15006
author: Morteza Seddighin
published in: Linear Algebra and its Applications
publication date: 2009-05-12T00:00:00Z
review text: Given an operator \(T\) on a Hilbert space \(H\), the first antieigenvalue of \(T\), also called the (real) cosine of \(T\), denoted by \(\mu_1(T)\) or \(\cos T\), was first defined by \textit{K. Gustafson} [Bull. Am. Math. Soc. 74, 488--492 (1968; Zbl 0172.40702)] to be \[ \mu_1(T)= \inf_{Tf\neq 0}\frac{\text{Re}(Tf,f)}{\| Tf\|\, \| f\|}\,. \] The author continues to explore two techniques used in antieigenvalue computations in previous papers. The first is basically a two nonzero component property for certain class of functionals. The second consists on converting the matrix optimization problems in statistics to a convex programming problem, finding the minimum of a convex function on the numerical range of an operator. The two techniques will permit generalizing some of the matrix optimization problems arising in statistics to strongly accretive operators on finite or infinite dimensional Hilbert spaces.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 62C20
Mathematics Subject Classification ID: 90C25
zbMATH DE Number: 5552958
zbMATH Keywords: antieigenvalue
zbMATH Keywords: antieigenvector
zbMATH Keywords: statistical efficiency
zbMATH Keywords: strongly accretive operator
zbMATH Keywords: numerical range
zbMATH Keywords: convex set
zbMATH Keywords: Hilbert space
zbMATH Keywords: convex programming
reviewed by: C. M.da Fonseca
MaRDI profile type: Publication
full work available at URL: j.laa.2008.05.007
OpenAlex ID: W1983584187
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DOI: 10.1016/J.LAA.2008.05.007
description: scientific article; zbMATH DE number 5552958