On the pure imaginary quaternionic solutions of the Hurwitz matrix equations
type: Item
instance of: scholarly article
title: On the pure imaginary quaternionic solutions of the Hurwitz matrix equations
zbMATH Open document ID: 1119.15014
author: Yik-Hoi Au-Yeung
author: Che-Man Cheng
published in: Linear Algebra and its Applications
publication date: 2007-02-14T00:00:00Z
review text: The number of \(n\times n\) pure imaginary quaternionic orthonormal matrices is analysed, i.e. the number \(p\) of the solutions of the Hurwitz matrix equations \[ T_iT_j^*+T_jT_i^*=2\delta_{ij}I,\quad i,j=1,\dots,p \] having the form \(sX\), where \(s\in\{1,i,j,k\}\) and \(X\) belonging to the real vector space of \(n\times n\) matrices with entries in the skew-field of real quaternions. The maximum number of these solutions is determined for \(n=2^m\) and \(m\neq0\)(mod 4). In the case \(m=0\) an evaluation of this number is given, and this is extended to a conjecture for the case \(m\equiv0\)(mod 4), \(m\neq0\). A construction of such numbers of pure imaginary matrices \(sX\) with \(X\) \(\{0,1,-1\}\)-matrices is provided.
reviewed by: Valeriu Prepeliţă
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15B33
zbMATH DE Number: 5126033
zbMATH Keywords: Hurwitz matrix equation
zbMATH Keywords: quaternions
zbMATH Keywords: Radon-Hurwitz number
zbMATH Keywords: pure imaginary quaternionic orthonormal matrices
MaRDI profile type: Publication
full work available at URL: j.laa.2006.06.005
OpenAlex ID: W2003667543
cites work: Vector fields on spheres
cites work: On Matrices Whose Real Linear Combinations are Nonsingular
cites work: On Matrices whose Nontrivial Real Linear Combinations are Nonsingular
cites work: Two formulas for the generalized radon-hurwitz number*
cites work: On the crossing rule
cites work: Isoclinic 𝑛-planes in Euclidean 2𝑛-space, Clifford parallels in elliptic (2𝑛-1)-space, and the Hurwitz matrix equations
DOI: 10.1016/J.LAA.2006.06.005
description: scientific article; zbMATH DE number 5126033