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Primitive spaces of matrices of bounded rank

Part of: Basic linear algebra

Published online by Cambridge University Press:  09 April 2009

M. D. Atkinson  and
S. Lloyd
M. D. Atkinson
Affiliation:
Department of Computing Mathematics, University College, Cardiff, Wales
S. Lloyd
Affiliation:
Department of Computing Mathematics, University College, Cardiff, Wales
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Abstract

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A weak canonical form is derived for vector spaces of m × n matrices all of rank at most r. This shows that the structure of such spaces is controlled by the structure of an associated ‘primitive’ space. In the case of primitive spaces it is shown that m and n are bounded by functions of r and that these bounds are tight.

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 30 , Issue 4 , April 1981 , pp. 473 - 482
Copyright
Copyright © Australian Mathematical Society 1981

References

Atkinson, M. D. and Lloyd, S. (1980), ‘Large spaces of matrices of bounded rank’, Quart. J. Math. Oxford Ser. 31, 253–262.CrossRefGoogle Scholar
Atkinson, M. D. and Stephens, N. M. (1978), ‘Spaces of matrices of bounded rank’, Quart. J. Math. Oxford Ser. 28, 205–207.Google Scholar
Flanders, H. (1962), ‘On spaces of linear transformations of bounded rank’, J. London Math. Soc. 37, 10–16.Google Scholar
Westwick, R. (1972), ‘Spaces of linear transformations of equal rank’, Linear Algebra and Appl. 5, 49–64.CrossRefGoogle Scholar