Geodesic
Linear Transformations on Grassmann Spaces
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 414-417

Voir la notice de l'article provenant de la source Cambridge University Press

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 Λr U. Let T be a linear transformation of Λr U 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 Λr U 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. 
Westwick, Roy. Linear Transformations on Grassmann Spaces. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 414-417. doi: 10.4153/CJM-1969-045-6
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[1] 1. Westwick, R., Linear transformations on Grassmann spaces, Pacific J. Math. 14 (1964), 1123–1127. Google Scholar

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