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Linear Transformations on Grassmann Spaces

Published online by Cambridge University Press:  20 November 2018

Roy Westwick
Roy Westwick*
Affiliation:
University of British Columbia, Vancouver, B.C.
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1. Let U denote an n-dimensional vector space over a field F and let Gnr denote the set of non-zero decomposable r-vectors of the Grassmann product space ΛrU. Let T be a linear transformation of ΛrU into itself which maps Gnr into itself. If F is algebraically closed, or if T is non-singular, then the structure of T is known. In this paper we show that if T is singular, then the image of ΛrU has a very special form with dimension equal to the larger of the integers r + 1 and n – r + 1. We give an example to show that this can occur.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 414 - 417
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Westwick, R., Linear transformations on Grassmann spaces, Pacific J. Math. 14 (1964), 1123–1127.Google Scholar