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Maximal extension for linear spaces of matrics with large rank
journal contribution
posted on 2023-06-08, 08:17 authored by Kewei ZhangFor 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.
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Publication status
- Published
Journal
Proceedings of the Royal Society of Edinburgh: Section A MathematicsISSN
0308-2105Publisher
Cambridge University PressExternal DOI
Issue
6Volume
131Page range
1481-1491Pages
11.0Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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