The geometrical meaning of the Kantorovich-Wielandt inequalities
type: Item
instance of: scholarly article
title: The geometrical meaning of the Kantorovich-Wielandt inequalities
zbMATH Open document ID: 0938.47026
DOI: 10.1016/S0024-3795(99)00106-8
published in: Linear Algebra and its Applications
publication date: 1999-11-29T00:00:00Z
review text: The main results of this paper are Theorem 1. For any symmetric positive definite matrix \(A\), \[ \cos\phi(A^2)= \sin\theta(A), \] where \(\phi(A)\) is the Gustafson operator angle and \(\theta(A)\) is the Kantorovich-Wielandt angle. Theorem 2. For any symmetric positive definite matrix \(A\), \[ \phi^2(A)+ \theta(A)={\pi\over 2}. \] Theorem 3. \(\cos\phi(A^*A)= \sin\theta(A)\) for any nonsingular \(n\times n\) matrix \(A\).
Mathematics Subject Classification ID: 47B37
zbMATH DE Number: 1371432
zbMATH Keywords: operator trigonometry
zbMATH Keywords: anti-eigenvector
zbMATH Keywords: symmetric positive definite matrix
zbMATH Keywords: Gustafson operator angle
zbMATH Keywords: Kantorovich-Wielandt angle
author: Karl Gustafson
reviewed by: K. Chandrasekhara Rao
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1371432