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Linear spaces of real matrices of large rank

  • Elmer G. Rees (a1)

Abstract

For every k1 0 < k < mn, there are linear spaces of real n × m matrices which have dimension (mk)(nk) 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.

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1Adams, J. F.. Vector fields on spheres. Ann. of Math. (2) 75 (1962), 603–32.
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.
3Adem, J.. On nonsingular bilinear maps II. Bol. Soc. Mat. Mexicana 16 (1971), 6470.
4Arbarello, E., Cornalba, M., Griffiths, P. A. and Harris, J.. Geometry of algebraic curves, Vol. 1 (New York: Springer, 1985).
5Bhattacharya, K., Firoozye, N. B., James, R. D. and Kohn, R. V.. Restrictions on mici ostructure. Proc. Roy. Soc. Edinburgh Sect. A (to appear).
6Flanders, H.. On spaces of linear transformations with bounded rank. J. London Math. Soc. 37 (1962), 1016.
7Handel, D.. On subspaces of tensor products containing no elements of rank one. J. Algebra 14 (1970), 523–7.
8Harris, J. and Tu, L. W.. On symmetric and skew-symmetric determinantal varieties. Topology 23 (1984), 7184.
9Hurwitz, A.. Uber der Komposition der quadratischer Formen. Math. Ann. 88 (1923), 125.
10Lam, K. Y.. Some interesting examples of nonsingular bilinear maps. Topology 16 (1977), 185–8.
11Mumford, D.. Algebraic geometry I, Complex projective varieties (New York: Springer, 1976).
12Radon, J.. Lineare Scharen orthogonalen Matrizen. Abh. Math. Sem. Univ. Hamburg 1 (1992), 114.
13Room, T. G.. The geometry of determinantal loci (Cambridge: Cambridge Universit Press, 1938).

Linear spaces of real matrices of large rank

  • Elmer G. Rees (a1)

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