Determinantal identities over commutative semirings
type: Item
instance of: scholarly article
title: Determinantal identities over commutative semirings
zbMATH Open document ID: 1057.15009
author: Phillip L. Poplin
author: R. E. Hartwig
published in: Linear Algebra and its Applications
publication date: 2004-08-04T00:00:00Z
review text: The authors present a development of determinantal identities over commutative semirings. This includes the following themes: 1. Positive and negative determinants; 2. Determinantal identities; 3. Adjoint matrix identities; 4. A generalization of the Cauchy-Binet theorem; 5. Compound matrices; 6. Identities over semirings; 7. Laplace's expansion over semiring and the Laplace theorem. There are many examples in the paper.
reviewed by: Nikolai I. Osetinski
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 16S50
zbMATH DE Number: 2081240
zbMATH Keywords: determinant
zbMATH Keywords: Laplace theorem
zbMATH Keywords: Cauchy-Binet theorem
zbMATH Keywords: determinantal identities
zbMATH Keywords: commutative semirings
zbMATH Keywords: adjoint matrix identities
zbMATH Keywords: compound matrices
MaRDI profile type: Publication
full work available at URL: j.laa.2004.02.019
OpenAlex ID: W2047285205
cites work: Q3254327
cites work: Q4700998
cites work: Inertia characteristics of self-adjoint matrix polynomials
DOI: 10.1016/J.LAA.2004.02.019
description: scientific article; zbMATH DE number 2081240