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Rank and border rank of Kronecker powers of tensors and Strassen's laser method

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You have full access to this open access article. We show that this tensor could potentially be used to show that the exponent of matrix multiplication is two. Download to read the full article text. Alman Limits on the Universal Method for Matrix Multiplication. In 34th Comp. CCC Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik. Williams a. In 9th Innov. Science Conf. Google Scholar. Williams b. Limits on all known and some unknown approaches to matrix multiplication. FOCS , — Williams A refined laser method and faster matrix multiplication. In Proc. SODA , — Ambainis , Y. Le Gall Fast matrix multiplication: limitations of the Coppersmith—Winograd method. Ballico , A. Bernardi , M. Gesmundo On the partially symmetric rank of tensor products of W-states and other symmetric tensors. Atti Accad. Lincei Rend. Lincei Mat. Bini Relations between exact and approximate bilinear algorithms. Calcolo 17 1 , 87— Bini , G. Romani Approximate solutions for the bilinear form computational problem. SIAM J. Fast Matrix Multiplication. Theory of Computing, Graduate Surveys 5 , 1— Lysikov On degeneration of tensors and algebras. Leibniz Int. Schloss Dagstuhl. Shokrollahi Algebraic complexity theory , volume of Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, Berlin. ISBN Christandl , F. Jensen Border rank is not multiplicative under the tensor product. Christandl , A. Zuiddam Tensor rank is not multiplicative under the tensor product. Christandl , P. Barriers for Fast Matrix Multiplication from Irreversibility. Theory of Computing 17 2 , 1— Umans A group theoretic approach to fast matrix multiplication. Science , number 2, — Conner , F. Gesmundo , J. Ventura a. Tensors with maximal symmetries. Conner, F. Gesmundo, J. Landsberg, E. Collectanea Mathematica 72 1 , 63— Conner , A. Landsberg b. Conner , H. Winograd Matrix multiplication via arithmetic progressions. Derksen On the nuclear norm and the singular value decomposition of tensors. Makam On non-commutative rank and tensor rank. Linear Multilinear Algebra 66 6 , — Efremenko , A. Garg , R. Wigderson Barriers for rank methods in arithmetic complexity. Fulton Young tableaux. With applications to representation theory and geometry , volume 35 of London Mathematical Society Student Texts. Cambridge University Press, Cambridge. Harris Representation theory: a first course , volume of Graduate Texts in Mathematics. Springer-Verlag, New York. Gay Rocky Mountain J. Gesmundo , C. Panova Geometric complexity theory and matrix powering. Stillman Macaulay 2, a software system for research in algebraic geometry Version 1. Teitler Math, Bull. Teitler Z An improved upper bound for the Waring rank of the determinant. Kopparty , G. In 35th Comp. Landsberg Geometry and complexity theory , volume of Cambridge Studies in Advanced Mathematics. Ottaviani Equations for secant varieties of Veronese and other varieties. Pura Appl. ISSN New lower bounds for the border rank of matrix multiplication. Powers of tensors and Fast Matrix Multiplication. Lenstra , H. Factoring Polynomials with Rational Coefficients. Ann 4 , Sohoni Geometric Complexity Theory. Towards explicit obstructions for embeddings among class varieties. Sage Developers Partial and total matrix multiplication. Stothers On the Complexity of Matrix Multiplication. Strassen Gaussian elimination is not optimal. Numerische mathematik 13 4 , — Rank and optimal computation of generic tensors. Relative bilinear complexity and matrix multiplication. Reine Angew. The asymptotic spectrum of tensors. Degeneration and complexity of bilinear maps: some asymptotic spectra. Algebra and complexity. Multiplying matrices faster than Coppersmith—Winograd. Download references. We thank the anonymous referees for their careful reading of the paper and useful suggestions. You can also search for this author in PubMed Google Scholar. Correspondence to Fulvio Gesmundo. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. Reprints and permissions. Conner, A. Rank and border rank of Kronecker powers of tensors and Strassen's laser method. Download citation. Received : 17 June Published : 18 December Anyone you share the following link with will be able to read this content:. Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative. Download PDF. Article PDF. On reverse-order law of tensors and its application to additive results on Moore—Penrose inverse Article 12 August Grothendieck constant is norm of Strassen matrix multiplication tensor Article 22 August Use our pre-submission checklist Avoid common mistakes on your manuscript. References J. Google Scholar J. Google Scholar M. Google Scholar A. Collectanea Mathematica 72 1 , 63—86 A. Landsberg Dept. View author publications. About this article. Cite this article Conner, A. Copy to clipboard. Search Search by keyword or author Search. Navigation Find a journal Publish with us Track your research.

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