Spanning-tree extensions of the Hadamard-Fischer inequalities
type: Item
instance of: scholarly article
title: Spanning-tree extensions of the Hadamard-Fischer inequalities
zbMATH Open document ID: 0619.05021
DOI: 10.1016/0024-3795(85)90131-4
author: Charles R. Johnson
author: Wayne Barrett
published in: Linear Algebra and its Applications
publication date: 1985-01-01T00:00:00Z
full work available at URL: http://purl.umn.edu/4967
review text: All possible graph-theoretic generalizations of a certain sort for the Hadamard-Fischer determinantal inequalities are determined. These involve ratios of products of principal minors which dominate the determinant. Furthermore, the cases of equality in these inequalities are characterized, and equality is possible for every set of values which can occur for the relevant minors. This relates recent work of the authors on positive definite completions and determinantal identities. When applied to the same collections of principal minors, earlier generalizations give poorer, more difficult to compute bounds than the present inequalities. Thus, this work extends, and in a certain sense completes, a series of generalizations of Hadamard-Fischer begun in the 1960s.
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A19
zbMATH DE Number: 4004206
zbMATH Keywords: determinantal identities
MaRDI profile type: Publication
OpenAlex ID: W2069298524
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Wikidata QID: Q127526577
description: scientific article; zbMATH DE number 4004206