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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.

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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