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Maximal extension for linear spaces of real matrices with large rank

Published online by Cambridge University Press:  12 July 2007

Kewei Zhang
Affiliation:
School of Mathematical Sciences, University of Sussex, Brighton BN1 9QH, UK (k.zhang@sussex.ac.uk)

Abstract

For every 0 < k < min{m,n} and any linear subspace E of real m × n matrices whose non-zero elements have rank greater than k, we show that there is a maximal extension Emax satisfying the same rank condition, and that the dimension of Emax is not less than (mk)(nk). We apply this result to the study of quasiconvex functions defined on the complement E of E in the form F(X) = f(PE(X)), where PE is the orthgonal projection to E.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2001

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