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Constructive noncommutative rank computation is in deterministic polynomial time. (arXiv:1512.03531v5 [cs.CC] UPDATED)
来源于:arXiv
We extend our techniques developed in our manuscript mentioned in the
subtitle to obtain a deterministic polynomial time algorithm for computing the
non-commutative rank together with certificates of linear spaces of matrices
over sufficiently large base fields.
The key new idea is a reduction procedure that keeps the blow-up parameter
small, and there are two methods to implement this idea: the first one is a
greedy argument that removes certain rows and columns, and the second one is an
efficient algorithmic version of a result of Derksen and Makam. Both methods
rely crucially on the regularity lemma in the aforementioned manuscript, and in
this note we improve that lemma by removing a coprime condition there.
arXiv:1508.00690 查看全文>>