The spectral theorem in quaternions
type: Item
instance of: scholarly article
title: The spectral theorem in quaternions
zbMATH Open document ID: 1030.15015
DOI: 10.1016/S0024-3795(03)00420-8
author: Douglas Farenick
author: Barbara A. F. Pidkowich
published in: Linear Algebra and its Applications
publication date: 2003-09-09T00:00:00Z
review text: An exposition of the spectral theory of normal matrices with quaternion entries is presented. The principal objective of the paper is to set down detailed proofs of the quaternionic spectral theorem in both the matrix-theoretic and abstract formulations. A second objective of the paper is to unite and to reflect upon some related issues that are crucial to the study of linear algebra over the quaternions: spectra, modules, and inner products. A few applications of the spectral theorem, such as the polar and singular value decompositions, are also explained.
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 1978107
zbMATH Keywords: quaternions
zbMATH Keywords: normal matrices
zbMATH Keywords: diagonal form
zbMATH Keywords: spectral theorem
zbMATH Keywords: spectra
zbMATH Keywords: modules
zbMATH Keywords: inner products
zbMATH Keywords: singular value decompositions
reviewed by: Rodica Covaci
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1978107