On the equality row rank and column rank
type: Item
instance of: scholarly article
title: On the equality row rank and column rank
zbMATH Open document ID: 0955.15001
published in: Expositiones Mathematicae
publication date: 2001-02-19T00:00:00Z
review text: The different proofs of the equality of the row rank and column rank of any rectangular matrix \(A\) over a field are discussed. It is proved using vector space duals that this equality holds also over any division ring if we mean by row rank of \(A\) the dimension of the left vector space generated by the rows of \(A\) and by column rank of \(A\) the dimension of the right vector space generated by the columns of \(A\). This proof shows that the equality of row rank and column rank is a consequence of the associativity of matrix multiplication over arbitrary rings rather than commutative properties of the entries of \(A\).
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 15A27
zbMATH DE Number: 1455780
zbMATH Keywords: row rank
zbMATH Keywords: column rank
zbMATH Keywords: commutativity
zbMATH Keywords: associativity
zbMATH Keywords: division ring
author: T. Y. Lam
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1455780