Geometry of skew-Hermitian matrices
type: Item
instance of: scholarly article
title: Geometry of skew-Hermitian matrices
zbMATH Open document ID: 1068.15023
author: Liping Huang
author: Zhe-Xian Wan
published in: Linear Algebra and its Applications
publication date: 2005-02-22T00:00:00Z
review text: The paper is organized as follows. In Section 2, automorphisms of division rings of generalized quaternions are studied. In Section 3, parallel to the geometry of Hermitian matrices maximal sets of rank 1 and rank 2 in the geometry of skew-Hermitian matrices are introduced and studied. In Section 4, when \(n= 2\), the affine space structure of any maximal set of rank 2 is introduced. In Section 5, Theorem 1.1 for the case \(n= 2\) is proved. Section 6 concludes the proof of Theorem 1.1. At the end of Section 6, it is pointed out that the condition \({\mathcal A}^{-1}\) preserving the adjacency in Theorem 1.1 can be omitted.
reviewed by: Yueh-er Kuo
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 51D20
Mathematics Subject Classification ID: 14L24
zbMATH DE Number: 2136675
zbMATH Keywords: Geometry of matrices
zbMATH Keywords: Skew-Hermitian matrix
zbMATH Keywords: Adjacency
zbMATH Keywords: Division ring with an involution
zbMATH Keywords: Division ring of generalized quaternions
zbMATH Keywords: rank
zbMATH Keywords: maximal set
MaRDI profile type: Publication
full work available at URL: j.laa.2004.08.030
OpenAlex ID: W2069193460
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DOI: 10.1016/J.LAA.2004.08.030
description: scientific article; zbMATH DE number 2136675