Principal values and principal subspaces of two subspaces of vector spaces with inner product
type: Item
instance of: scholarly article
title: Principal values and principal subspaces of two subspaces of vector spaces with inner product
zbMATH Open document ID: 0971.15001
author: Ice Risteski
author: K. Trenčevski
published in: Beiträge zur Algebra und Geometrie
publication date: 2001-01-09T00:00:00Z
full work available at URL: https://eudml.org/doc/225640
full work available at URL: 20.html
review text: Two subspaces \(\Sigma_1\) and \(\Sigma_2\) of arbitrary dimensions in the Euclidean space \(E_n\) are defined. It is proved that the angle between these two subspaces \(\varphi(\Sigma_1, \Sigma_2)\) is equal to the angle between their orthogonal complements \(\Sigma_1^*\) and \(\Sigma_2^*\). Matrices \(A_1\) and \(A_2\) whose vector rows generate the subspace \(\Sigma_1\) and \(\Sigma_2\), respectively, are used for the definitions of principal values as common eigenvalues of these matrices. The principal subspaces or principal directions for the eigenvalues with multipolarity \(1\) are introduced as the orthogonal eigenspaces resulting from unique decomposition of the subspaces \(\Sigma_1\) and \(\Sigma_2\). As a final result the canonical matrix for two subspaces \(\Sigma_1\) and \(\Sigma_2\) is given together with its relation to the duality principle.
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 15A63
Mathematics Subject Classification ID: 51N20
zbMATH DE Number: 1549918
zbMATH Keywords: principal values
zbMATH Keywords: principal subspaces
zbMATH Keywords: principal direction
zbMATH Keywords: angle between two subspaces
zbMATH Keywords: duality principle
zbMATH Keywords: eigenvalues
zbMATH Keywords: eigenspaces
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1549918