On the product of convex combinations and the Kantorovich inequality
type: Item
instance of: scholarly article
title: On the product of convex combinations and the Kantorovich inequality
zbMATH Open document ID: 0626.15013
DOI: 10.1016/S0024-3795(87)90309-0
author: Sin-Chung Chang
published in: Linear Algebra and its Applications
publication date: 1987-01-01T00:00:00Z
review text: The paper deals with the problem to find the maximum and minimum of the product of two positive definite quadratic forms as a function on the unit sphere in n-dimensional complex space. If the two quadratic forms have a simultaneous diagonalization then the above problem is equivalent with the problem to maximize resp. minimize the product of two convex combinations of two sets of n real numbers with the same weights as a function of the weights. In this case a formula for the maximum and minimum is given thus relating to a classical inequality of Kantorovich for products of two convex combinations of positive numbers and their inverses with the same weights. In the general case estimates for the quotient between the maximal and minimal value are given.
Mathematics Subject Classification ID: 15A63
Mathematics Subject Classification ID: 15A45
zbMATH DE Number: 4017104
zbMATH Keywords: product of convex combinations
zbMATH Keywords: Kantorovich inequality
zbMATH Keywords: positive definite quadratic forms
reviewed by: Tage Bai Andersen
MaRDI profile type: Publication
cites work: Q5331504
cites work: On a Generalization of an Inequality of L. V. Kantorovich
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cites work: Matrix Analysis
cites work: Generalizations of two inequalities involving Hermitian forms
description: scientific article; zbMATH DE number 4017104