Surjections on grassmannians preserving pairs of elements with bounded distance

M.H. Lim

Document Type

Article

Publication Date

1-1-2010

Abstract

Let m and k be two fixed positive integers such that m > k >= 2. Let V be a left vector space over a division ring with dimension at least m + k + 1. Let G(m) (V) be the Grassmannian consisting of all m-dimensional subspaces of V. We characterize surjective mappings T from g, (V) onto itself such that for any A, B in 9,,(V), the distance between A and B is not greater than k if and only if the distance between T(A) and T(B) is not greater than k. (C) 2009 Elsevier Inc. All rights reserved.

Publication Title

Linear Algebra and its Applications

Volume

432

Issue

7

Publisher

Elsevier

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