Maximal extension for linear spaces of real matrices with large rank

Author: Zhang K.

Source: Proceedings Section A: Mathematics - Royal Society of Edinburgh, Volume 131, Number 6, 14 December 2001 , pp. 1481-1491(11)

Publisher: Royal Society of Edinburgh

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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 E_max satisfying the same rank condition, and that the dimension of E_max 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(P_E(X)), where P_E is the orthgonal projection to E.

Document Type: Research article

Publication date: 2001-12-14