Square of an \(n\)-vector in an \(E_n\)
type: Item
instance of: scholarly article
title: Square of an \(n\)-vector in an \(E_n\)
zbMATH Open document ID: 0924.15024
DOI: 10.1007/BF03041921
author: Gaston Casanova
published in: Advances in Applied Clifford Algebras
publication date: 1999-11-07T00:00:00Z
review text: The paper presents elementary computations for real Clifford algebras (which can be easily generalized to other fields using appropriate notions). The author computes the square of \(A_n\) which is defined as the product (in the associated Clifford algebra) of an orthogonal basis of a real quadratic space of dimension \(n\), and shows that if \(A_r\) (\(r\leq n\)) denotes the product of the \(r\) first vectors of the given basis and \(A_{n-r}\) is the product of the remaining ones, then \(A_n\), \(A_r\) and \(A_{n-r}\) pairwise commute if and only if \((A_n)^2=(A_r)^2(A_{n-r})^2\).
reviewed by: Philippe Elbaz-Vincent
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 15A63
zbMATH DE Number: 1240575
zbMATH Keywords: real Clifford algebra
zbMATH Keywords: \(n\)-vector
zbMATH Keywords: orthogonal basis
zbMATH Keywords: quadratic space
MaRDI profile type: Publication
cites work: Counter-examples in Clifford algebras
cites work: On the logarithms in the Clifford algebras \(CL(n,0)\)
full work available at URL: https://doi.org/10.1007/bf03041921
OpenAlex ID: W2517775722
description: scientific article; zbMATH DE number 1240575