Maximal extension for linear spaces of real matrices with large rank

Author： Zhang Kewei  

Publisher： Royal Society of Edinburgh

ISSN： 1473-7124

Source： Proceedings Section A: Mathematics - Royal Society of Edinburgh, Vol.131, Iss.6, 2001-12, pp. : 1481-1491

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

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