237
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

The Geometry of Rank Decompositions of Matrix Multiplication I: 2 × 2 Matrices

, , &

References

  • [Ballard et al. XX] G. Ballard, C. Ikenmeyer, J. M. Landsberg, and N. Ryder. “The Geometry of Rank Decompositions of Matrix Multiplication II: 3x3 Matrices.” Preprint.
  • [Bermudez et al. 14] Bermudez, S. Garibaldi, and V. Larsen. “Linear Preservers and Representations with a 1-Dimensional Ring of Invariants.” Trans. Amer. Math. Soc. 366:9 (2014), 4755–4780. MR 3217699
  • [Burichenko 14] V. P. Burichenko. “On Symmetries of the Strassen Algorithm.” CoRR abs/1408.6273, 2014.
  • [Burichenko 15] V. P. Burichenko. “Symmetries of Matrix Multiplication Algorithms. I.” CoRR abs/1508.01110, 2015.
  • [Comon 02] P. Comon. “Tensor Decompositions, State of the Art and Applications.” In Mathematics in Signal Processing V, edited by J. G. McWhirter and I. K. Proudler, pp. 1–24. Oxford, UK: Clarendon Press, 2002. arXiv:0905.0454v1.
  • [de Groote 78] H. F. de Groote. “On Varieties of Optimal Algorithms for the Computation of Bilinear Mappings. I. The Isotropy Group of a Bilinear Mapping.” Theoret. Comput. Sci. 7:1 (1978), 1–24. MR 0506377
  • [Gesmundo 16] F. Gesmundo. “Geometric Aspects of Iterated Matrix Multiplication.” J. Algebra 461 (2016), 42–64. MR 3513064
  • [Landsberg 12] J. M. Landsberg. Tensors: Geometry and Applications, Graduate Studies in Mathematics, vol. 128. Providence, RI: American Mathematical Society, 2012. MR 2865915.
  • [Shitov 17] Y. Shitov. “A Counterexample to Comon's Conjecture.” arXiv:1705.08740 (2017).
  • [Strassen 69] V. Strassen. “Gaussian Elimination is not Optimal.” Numer. Math. 13 (1969), 354–356. MR 40 #2223

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.