Maximal extension for linear spaces of matrics with large rank

Zhang, Kewei (2001) Maximal extension for linear spaces of matrics with large rank. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 131 (6). pp. 1481-1491. ISSN 0308-2105

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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 Exs22A5 of E in the form F(X) = f(PExs22A5(X)), where PExs22A5 is the orthgonal projection to Exs22A5.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Kewei Zhang
Date Deposited: 06 Feb 2012 20:56
Last Modified: 10 Jul 2012 12:02
URI: http://sro.sussex.ac.uk/id/eprint/28769
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