Evenness of the Jordan structure of block quaternions with real spectra and its computational consequences
type: Item
instance of: scholarly article
title: Evenness of the Jordan structure of block quaternions with real spectra and its computational consequences
zbMATH Open document ID: 0944.15016
published in: Computational Mathematics and Mathematical Physics
publication date: 2000-04-05T00:00:00Z
review text: The author shows that the block quaternion is an even order complex matrix of a special block form. It has been known that, if such a matrix has a real eigenvalue, then its algebraic multiplicity is even. It is proved that a stronger property is valid: The whole part of the Jordan structure associated with the real eigenvalues of a block quaternion is even. This implies that the number of Jordan blocks associated with a real eigenvalue is even. The consequences of this property related to the numerical solution of eigenvalue problems for block quaternions are discussed.
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 1427861
zbMATH Keywords: complex matrix
zbMATH Keywords: block quaternion
zbMATH Keywords: real eigenvalue
zbMATH Keywords: algebraic multiplicity
zbMATH Keywords: Jordan structure
author: Kh. D. Ikramov
reviewed by: A. Tret'yakov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1427861