A short proof of Hua's fundamental theorem of the geometry of Hermitian matrices.
type: Item
instance of: scholarly article
title: A short proof of Hua's fundamental theorem of the geometry of Hermitian matrices.
zbMATH Open document ID: 1036.15002
DOI: 10.1016/S0723-0869(03)80012-9
author: Peter Šemrl
author: H. Radjavi
published in: Expositiones Mathematicae
publication date: 2003-10-28T00:00:00Z
review text: The authors give a new and simple proof for the fundamental theorem of the geometry of Hermitian matrices due to Loo-Keng Hua. This theorem describes for \(n\geq 2\) all bijections of \(H_n\) (i.e. the set of Hermitian \(n\times n\) matrices over the complex numbers) onto itself which preserve adjacency in both directions. Here, as usual, two matrices \(A,B\in H_n\) are said to be adjacent if \(\text{rank }(A-B)=1\).
reviewed by: Hans Havlicek
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 1930885
zbMATH Keywords: Hermitian matrix
zbMATH Keywords: adjacency
zbMATH Keywords: geometry of matrices
MaRDI profile type: Publication
cites work: Geometries of Matrices. I 1 Arithmetical Construction
cites work: Adjacency preserving maps on matrices and operators
cites work: On Hua's fundamental theorem of the geometry of rectangular matrices
cites work: Q4885576
full work available at URL: s0723-0869(03)80012-9
OpenAlex ID: W2075869743
description: scientific article; zbMATH DE number 1930885