References
- Fortin M, Reutenauer C. Commutative/non-commutative rank of linear matrices and subspaces of matrices of low rank. Sém Lothar Combin. 2004;52:B52f.
- Garg A, Gurvits L, Oliveira R, et al. A deterministic polynomial time algorithm for non-commutative rational identity testing. arXiv:1511.03730; 2015.
- Ivanyos G, Qiao Y, Subrahmanyam KV. Non-commutative Edmonds’ problem and matrix semi-invariants. arXiv:1508.00690 [cs.DS]; 2015.
- Eisenbud D, Harris J. Vector spaces of matrices of low rank. Adv Math. 1988;70:135–155.
- Derksen H, Makam V. Polynomial degree bounds for matrix semi-invariants. arXiv:1512.03393 [math.RT]; 2015.
- Domokos M. Relative invariants of 3×3 matrix triples. Linear Multilinear Algebra. 2000;47:175–190.
- Ivanyos G, Qiao Y, Subrahmanyam KV. Constructive noncommutative rank computation in deterministic polynomial time over fields of arbitrary characteristics. tt arXiv:1512.03531 [cs.CC]; 2015.
- Bergman G. Rational relations and rational identities in division rings. I. J Algebra. 1976;43:252–266.
- Hrubeš P, Wigderson A. Non-commutative arithmetic circuits with division, ITCS’14, Princeton, NJ, USA; 2014.
- Landsberg JM. Nontriviality of equations and explicit tensors in Cm ⊗Cm ⊗ Cm of border rank at least 2m – 2. J Pure Appl Algebra. 2015;219:3677–3684.
- Amitsur SA. The T-ideals of the free ring. J London Math Soc. 1955;30:470–475.
- Amitsur SA. On central division algebras. Israel J Math. 1972;12:408–420.
- Amitsur SA. The generic division rings. Israel J Math. 1974;17:241–247.
- Cohn PM. Skew fields. Theory of general division rings. Vol. 57, Encyclopedia of mathematics and its applications. Cambridge: Cambridge University Press; 1995.
- Jacobson N. PI-algebras. Vol. 441, Lecture notes in mathematics. Berlin: Springer-Verlag; 1975.
- Posner EC. Prime rings satisfying a polynomial identity. Proc Amer Math Soc. 1960;11:180–184.
- Jacobson N. Basic algebra. II. 2nd ed. New York (NY): W. H. Freeman and Company; 1989.
- Flanders H. On spaces of linear transformations with bounded rank. J London Math Soc. 1962;37:10–16.
- Bergman G. Rational relations and rational identities in division rings. II. J Algebra. 1976;43:267–297.
- Gurvits L. Classical complexity and quantum entanglement. J Comp Syst Sci. 2004;69:448–484.
- Landsberg JM. New lower bounds for the rank of matrix multiplication. SIAM J Comput. 2014;43:144–149.
- Massarenti A, Ravioli E. The rank of n×n matrix multiplication is at least 3n2−2√2n3/2–3n. Linear Algebra Appl. 2013;438:4500–4509.
- Massarenti A, Ravioli E. Corrigendum to “The rank of n×n matrix multiplication is at least 3n2−2√2n3/2–3n” [Linear Algebra Appl. 438 (11) (2013) 4500--4509]. Linear Algebra Appl. 2014;445:369–371.
- Landsberg JM. Tensors: geometry and applications. Vol. 128, Graduate studies in mathematics. Providence (RI): American Mathematical Society; 2012.