Maximizing bilinear forms subject to linear constraints
type: Item
instance of: scholarly article
title: Maximizing bilinear forms subject to linear constraints
zbMATH Open document ID: 0832.65052
DOI: 10.1016/0024-3795(94)90465-0
author: Steven J. Leon
published in: Linear Algebra and its Applications
publication date: 1996-03-05T00:00:00Z
full work available at URL: http://hdl.handle.net/20.500.11850/68952
review text: Let \(A \in\mathbb{R}^{m \times n}\), \(B \in\mathbb{R}^{m \times p}\), \(C \in\mathbb{R}^{k \times m}\), \(G \in\mathbb{R}^{p \times n}\), \(d \in\mathbb{R}^k\), \(h \in\mathbb{R}^p\). The author studies the problem of maximizing the bilinear form \((x^T Ay)/(|x|\cdot |y|)\), or its absolute value subject to linear constraints of the form \(Cx = d\), \(Gy = h\) or of the form \(Cx \in R(D)\), \(Gy \in R(H)\), where \(R(D)\) and \(R(H)\) represent the column spaces of the matrices \(D \in\mathbb{R}^{k \times r}\) and \(H \in\mathbb{R}^{p \times \ell}\). Finally, he determines the angle between two subspaces of \(\mathbb{R}^m\) and the canonical correlations for the pair \((A,B)\) subject to the linear equality constraints \(Cx = d\), \(Gy = h\).
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 90C20
zbMATH DE Number: 698651
zbMATH Keywords: quadratic programming
zbMATH Keywords: bilinear form
zbMATH Keywords: canonical correlations
zbMATH Keywords: linear equality constraints
reviewed by: Dorel I. Duca
MaRDI profile type: Publication
OpenAlex ID: W2024045684
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description: scientific article; zbMATH DE number 698651