A remark on constructions of certain normed and nonsingular bilinear maps
type: Item
instance of: scholarly article
title: A remark on constructions of certain normed and nonsingular bilinear maps
zbMATH Open document ID: 0549.05042
author: T. Bier
published in: Proceedings of the Japan Academy. Series A
publication date: 1983-01-01T00:00:00Z
review text: For what triples (a,b,c) does there exist an \({\mathbb{R}}\)-bilinear map \(f: {\mathbb{R}}^ a\times {\mathbb{R}}^ b\to {\mathbb{R}}^ c\) with \(\| f(x,y)\| =\| x\| \cdot \| y\|\)? Here \(\| z\| =z^ 2_ 1+...+z^ 2_ d\) for \(z\in {\mathbb{R}}^ d\). The paper under review announces a graph-theoretical approach to the classical problem above for the special case \(b=c=2^ m\). The same methods are also used for the following related question: For what triples (a,b,c) does there exist an \({\mathbb{R}}\)-bilinear map \(f: {\mathbb{R}}^ a\times {\mathbb{R}}^ b\to {\mathbb{R}}^ c\) such that \(f(x,y)=0\) implies \(x=0\) or \(y=0?\)
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 15A63
zbMATH DE Number: 3875326
zbMATH Keywords: composition of quadratic forms
zbMATH Keywords: bilinear forms
reviewed by: Hans-Jochen Bartels
MaRDI profile type: Publication
full work available at URL: pjaa.59.328
OpenAlex ID: W1968582823
cites work: A distribution invariant for association schemes and strongly regular graphs
cites work: Gruppentheoretischer Beweis des Satzes von Hurwitz-Radon über die Komposition quadratischer Formen
cites work: Q5181734
DOI: 10.3792/PJAA.59.328
description: scientific article; zbMATH DE number 3875326