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Primitive spaces of matrices of bounded rank. II

Part of: Basic linear algebra

Published online by Cambridge University Press:  09 April 2009

M. D. Atkinson
M. D. Atkinson
Affiliation:
Department of Computing Mathematics University CollegeCardiff, U. K.
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Abstract

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The classification of spaces of matrices of bounded rank is known to depend upon ‘primitive’ spaces, whose structure is considerably restricted. A characterisation of an infinite class of primitive spaces is given. The result is then applied to obtain a complete description of spaces whose matrices have rank at most 3.

MSC classification

Secondary: 15A30: Algebraic systems of matrices 15A03: Vector spaces, linear dependence, rank
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 34 , Issue 3 , June 1983 , pp. 306 - 315
Copyright
Copyright © Australian Mathematical Society 1983

References

Atkinson, M. D. and Lloyd, S. (1980), ‘Large spaces of matrices of bounded rank’, Quart. J. Math. Oxford Ser. 31, 253–262.Google Scholar
Atkinson, M. D. and Lloyd, S. (1981), ‘Primitive spaces of matrices of bounded rank’, J. Austral. Math. Soc. (Ser. A) 30, 473–482.CrossRefGoogle Scholar
Atkinson, M. D. and Westwick, R., ‘Spaces of linear transformations of equal rank’, Linear and Multilinear Algebra, to appear.Google Scholar
Flanders, H. (1962), ‘On spaces of linear transformations of bounded rank’, J. London Math. Soc. 37, 10–16.CrossRefGoogle Scholar
Gauger, M. A. (1973), ‘On the classification of metabelian Lie algebras’, Trans. Amer. Math. Soc. 179, 293–329.CrossRefGoogle Scholar
Lloyd, S. (1980), Computation of bilinear forms and canonical forms of tensors (Ph. D. thesis, Cardiff).Google Scholar
Vaughan-Lee, M. R. (1974), Breadth and commutator subgroups of p-groups’, J. Algebra 32, 278–285.Google Scholar
Westwick, R. (1972), ‘Spaces of linear transformations of equal rank’, Linear Algebra and Appl. 5, 49–64.CrossRefGoogle Scholar