Preservers of pairs of bivectors with bounded distance
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 x n alternate matrices over a field with at least th...
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| Main Authors: | , |
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| Format: | Article |
| Published: |
Elsevier
2009
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| Subjects: | |
| Online Access: | http://library.oum.edu.my/repository/284/ |
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| Summary: | 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 x 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. (Authors' abstract) |
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