A Remark on the Rank of Positive Semidefinite Matrices Subject to Affine Constraints
نویسندگان
چکیده
منابع مشابه
A Remark on the Rank of Positive Semidefinite Matrices Subject to Affine Constraints
Let K n be the cone of positive semideenite n n matrices and let A be an aane subspace of the space of symmetric matrices such that the intersection K n \ A is non-empty and bounded. Suppose that n 3 and that codim A = ? r+2 2 for some 1 r n?2. Then there is a matrix X 2 K n \A such that rank X r. We give a short geometric proof of this result, use it to improve a bound on realizability of weig...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2001
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s004540010074