Maximal extension for linear spaces of real matrices with large rank
Published online by Cambridge University Press: 12 July 2007
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 (m – k)(n – k). 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
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 6 , December 2001 , pp. 1481 - 1491
- Copyright
- Copyright © Royal Society of Edinburgh 2001
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