On a generalized Fan inequality
type: Item
instance of: scholarly article
title: On a generalized Fan inequality
zbMATH Open document ID: 0546.15007
DOI: 10.1016/0024-3795(84)90214-3
published in: Linear Algebra and its Applications
publication date: 1984-01-01T00:00:00Z
review text: The author shows that some classes of matrices can all be characterized by the same determinantal inequality, called by the author a generalized Fan inequality, and which derives from the Hadamard-Fisher type of inequality for a product of principal minors. The classes include \(\omega\),\(\tau\),M,R,V, and other, matrices. The study of these inequalities for M-matrices was initiated by Ky Fan, whence the title chosen by the author for his paper.
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 3869528
zbMATH Keywords: Hadamard inequality
zbMATH Keywords: M-matrix
zbMATH Keywords: Fischer inequality
zbMATH Keywords: omega-matrix
zbMATH Keywords: tau- matrix
zbMATH Keywords: determinantal inequality
zbMATH Keywords: generalized Fan inequality
zbMATH Keywords: principal minors
author: Volker Mehrmann
reviewed by: Robert C. Thompson
MaRDI profile type: Publication
full work available at URL: 0024-3795(84)90214-3
OpenAlex ID: W2072401625
cites work: Q3276750
cites work: Q3943082
cites work: Weakly sign-symmetric matrices and some determinantal inequalities
cites work: Cyclic and diagonal products on a matrix
cites work: The Hadamard-Fischer inequality for a class of matrices defined by eigenvalue monotonicity
cites work: NOTE ON M-MATRICES
cites work: Q3261425
cites work: On weakly sign-symmetric matrices
cites work: Necessary conditions and a sufficient condition for the Fischer-Hadamard inequalities
cites work: A property of sign-symmetric matrices
cites work: Q4745955
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description: scientific article; zbMATH DE number 3869528