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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

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