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On the space of matrices of given rank

Published online by Cambridge University Press:  20 January 2009

M. C. Crabb  and
D. L. Gonçalves
M. C. Crabb
Affiliation:
Department of MathematicsUniversity of AberdeenAberdeen AB9 2TYScotland
D. L. Gonçalves
Affiliation:
Instituto de Matemática e EstatísticaUniversidade de São PauloSão PauloBrazil
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Let V and W be finite dimensional real vector spaces, k≧0 an integer. We write L(V, W) for the space of all linear maps V→W and Lk(V, W) for the subspace of maps with kernel of dimension k; in particular, L0(V, W) is the open subspace of injective linear maps. Thus Lk(ℝn, ℝn) is the space of n × n-matrices of rank n – k in the title. We also need the notation Gk(V) for the Grassmann manifold of K-dimensional subspaces of V.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , Issue 1 , February 1989 , pp. 99 - 105
Copyright
Copyright © Edinburgh Mathematical Society 1989

References

REFERENCES

1.Crabb, M. C., On the stable splitting of U(n) and ΩU(n), in Algebraic Topology Barcelona 1986 (Springer Lecture Notes in Math. 1298, 1987), 35–53.CrossRefGoogle Scholar
2.Husemoller, D., Fibre Bundles (McGraw-Hill, New York, 1966).CrossRefGoogle Scholar
3.James, I. M., The Topology of Stiefel Manifolds (Cambridge University Press, 1976).Google Scholar
4.James, I. M., General Topology and Homotopy Theory (Springer-Verlag, New York, 1984).CrossRefGoogle Scholar
5.Miller, H., Stable splittings of Stiefel manifolds, Topology 24 (1985), 411–419.CrossRefGoogle Scholar