Constructive noncommutative rank computation in deterministic polynomial time over fields of arbitrary characteristics.
Gábor Ivanyos, Youming Qiao, Katta V Subrahmanyam · arXiv (Cornell University) · 2015
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