Corpus ID: 237502764

Symbolic determinant identity testing and non-commutative ranks of matrix Lie algebras

  title={Symbolic determinant identity testing and non-commutative ranks of matrix Lie algebras},
  author={G{\'a}bor Ivanyos and Tushant Mittal and Youming Qiao},
One approach to make progress on the symbolic determinant identity testing (SDIT) problem is to study the structure of singular matrix spaces. After settling the noncommutative rank problem (Garg–Gurvits–Oliveira–Wigderson, Found. Comput. Math. 2020; Ivanyos–Qiao–Subrahmanyam, Comput. Complex. 2018), a natural next step is to understand singular matrix spaces whose non-commutative rank is full. At present, examples of such matrix spaces are mostly sporadic, so it is desirable to discover them… Expand
1 Citations
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A complexity analysis of an existing algorithm due to Gurvits (J Comput Syst Sci 69(3):448–484, 2004 ), who proved it was polynomial time for certain classes of inputs, that is extended to actually approximate capacity to any accuracy in polynometric time. Expand
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Subspace arrangements, graph rigidity and derandomization through submodular optimization
A deterministic, strongly polynomial time algorithm for computing the matrix rank for a class of symbolic matrices (whose entries are polynomials over a field) that is seen as a generalization of the well-known deterministic algorithm for the latter problem. Expand
Constructive non-commutative rank computation is in deterministic polynomial time
The techniques developed in Ivanyos et al. (2017) are extended to obtain a deterministic polynomial-time algorithm for computing the non-commutative rank of linear spaces of matrices over any field to improve that lemma by removing a coprime condition there. Expand
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This paper considers the non-commutative version of Edmonds’ problem: compute the rank of T over the free skew field by using an algorithm of Gurvits, and assuming the above bound of sigma for R(n, m) over Q, deciding whether or not T has non-Commutative rank < n over Q can be done deterministically in time polynomial in the input size and $$sigma}$$σ. Expand
, and AviWigderson . Operator scaling : Theory and applications
  • Found . Comput . Math . Lie Groups , Lie Algebras , and Representations
  • 2015
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