Invariant tolerance relations on positive definite matrices
type: Item
instance of: scholarly article
title: Invariant tolerance relations on positive definite matrices
zbMATH Open document ID: 1464.15009
author: Yongdo Lim
published in: Linear Algebra and its Applications
publication date: 2021-04-24T00:00:00Z
review text: The author considers the Cartan-Hadamard Riemannian manifold of \(N\times N\) positive definite Hermitian matrices whose tolerance classes are determined by a closed linear form of their Riemannian geodesics and introduce several invariant tolerance relations. It is shown for one of such relations that it admits a linearly independent ordered pair only when the matrix size is even, and the relation on determinant one matrices is characterized by the geometric mean formula \(A\ast B = \frac{A+B}{\sqrt[N]{\det(A+B)}}\).
reviewed by: Andreas Arvanitoyeorgos
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 47A64
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 7337637
zbMATH Keywords: positive definite matrix
zbMATH Keywords: geometric mean
zbMATH Keywords: invariant tolerance relation
MaRDI profile type: Publication
full work available at URL: j.laa.2021.02.008
OpenAlex ID: W3126179669
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DOI: 10.1016/J.LAA.2021.02.008
description: scientific article; zbMATH DE number 7337637