Article ID Journal Published Year Pages File Type
4602209 Linear Algebra and its Applications 2009 10 Pages PDF
Abstract

We extend Liu’s fundamental theorem of the geometry of alternate matrices to the second exterior power of an infinite dimensional vector space and also use her theorem to characterize surjective mappings T from the vector space V of all n×n alternate matrices over a field with at least three elements onto itself such that for any pair A, B in V, rank(A-B)⩽2k if and only if rank(T(A)-T(B))⩽2k, where k is a fixed positive integer such that n⩾2k+2 and k⩾2.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory