\(p\)-adic matrix valued inequalities
type: Item
instance of: scholarly article
title: \(p\)-adic matrix valued inequalities
zbMATH Open document ID: 0577.15019
DOI: 10.1016/0024-3795(85)90257-5
author: Robert C. Thompson
published in: Linear Algebra and its Applications
publication date: 1985-01-01T00:00:00Z
review text: The author defines the \(p\)-adic matrix absolute value \(\vert A\vert_p\) to be the diagonal matrix of powers of \(p\) corresponding to torsion numbers. He proves \[ \vert A+B\vert_p\leq \max (\vert A\vert_p + \vert B\vert_p) \leq U \vert A\vert_p U^*+V\vert B\vert_pV^* \] for permutation matrices \(U\), \(V\) and conjectures, giving a \(3\times 3\) proof which he feels works in general, for some unitary \(U\), \(V\), \[ \vert AB\vert_p\leq \tfrac12(U\vert A\vert_p \vert B\vert_p U^* + V \vert A\vert_p \vert B\vert_p V^*). \]
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 15B33
zbMATH DE Number: 3922884
zbMATH Keywords: matrix valued inequalities
zbMATH Keywords: triangle inequality
zbMATH Keywords: norm inequality
zbMATH Keywords: p-adic matrix absolute value
zbMATH Keywords: torsion numbers
reviewed by: Ki Hang Kim
MaRDI profile type: Publication
full work available at URL: 0024-3795(85)90257-5
OpenAlex ID: W2033299580
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description: scientific article; zbMATH DE number 3922884