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Spaces of Singular Matrices and Matroid Parity

✍ Scribed by Boaz Gelbord; Roy Meshulam

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
99 KB
Volume
23
Category
Article
ISSN
0195-6698

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✦ Synopsis

Let V be a linear space of even dimension n over a field F of characteristic 0. A subspace W ⊂ ∧ 2 V is maximal singular if rank(w) ≤ n -1 for all w ∈ W and any W W ⊂ ∧ 2 V contains a nonsingular matrix.

It is shown that if W ⊂ ∧ 2 V is a maximal singular subspace which is generated by decomposable elements then dim W ≥ 3n 2 -3 and that this bound is sharp. The main tool in the proof is the Lovász Matroid Parity Theorem.

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