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Linear spaces of real matrices of large rank

Published online by Cambridge University Press:  14 November 2011

Elmer G. Rees
Elmer G. Rees
Affiliation:
Department of Mathematics and Statistics, James Clerk Maxwell Building, King's Buildings, Edinburgh EH9 3JZ, Scotland, U.K.
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Abstract

For every k1 0 < k < m ≧ n, there are linear spaces of real n × m matrices which have dimension (m − k)(n − k) and every nonzero element has rank greater than k. Examples of such spaces are constructed and conditions are given under which they have the largest possible dimension.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 1 , 1996 , pp. 147 - 151
Copyright
Copyright © Royal Society of Edinburgh 1996

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References

1Adams, J. F.. Vector fields on spheres. Ann. of Math. (2) 75 (1962), 603–32.CrossRefGoogle Scholar
2Adams, J. F., Lax, P. and Phillips, R.. On matrices whose real linear combinations are non-singular. Proc. Amer. Math. Soc. 16 (1965), 318–22.Google Scholar
3Adem, J.. On nonsingular bilinear maps II. Bol. Soc. Mat. Mexicana 16 (1971), 64–70.Google Scholar
4Arbarello, E., Cornalba, M., Griffiths, P. A. and Harris, J.. Geometry of algebraic curves, Vol. 1 (New York: Springer, 1985).CrossRefGoogle Scholar
5Bhattacharya, K., Firoozye, N. B., James, R. D. and Kohn, R. V.. Restrictions on mici ostructure. Proc. Roy. Soc. Edinburgh Sect. A (to appear).Google Scholar
6Flanders, H.. On spaces of linear transformations with bounded rank. J. London Math. Soc. 37 (1962), 10–16.CrossRefGoogle Scholar
7Handel, D.. On subspaces of tensor products containing no elements of rank one. J. Algebra 14 (1970), 523–7.CrossRefGoogle Scholar
8Harris, J. and Tu, L. W.. On symmetric and skew-symmetric determinantal varieties. Topology 23 (1984), 71–84.CrossRefGoogle Scholar
9Hurwitz, A.. Uber der Komposition der quadratischer Formen. Math. Ann. 88 (1923), 1–25.CrossRefGoogle Scholar
10Lam, K. Y.. Some interesting examples of nonsingular bilinear maps. Topology 16 (1977), 185–8.CrossRefGoogle Scholar
11Mumford, D.. Algebraic geometry I, Complex projective varieties (New York: Springer, 1976).Google Scholar
12Radon, J.. Lineare Scharen orthogonalen Matrizen. Abh. Math. Sem. Univ. Hamburg 1 (1992), 1–14.CrossRefGoogle Scholar
13Room, T. G.. The geometry of determinantal loci (Cambridge: Cambridge Universit Press, 1938).Google Scholar