On the Geometry of Border Rank Decompositions for Matrix Multiplication and Other Tensors with Symmetry

DOI10.1137/16M1067457zbMath1365.15034arXiv1601.08229MaRDI QIDQ5347291

Mateusz Michałek, Joseph M. Landsberg

Publication date: 23 May 2017

Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.08229

zbMATH Keywords

tensornormal formsdeterminantcommuting matricesborder rankmatrix multiplication complexityStrassen's equations

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Homogeneous spaces and generalizations (14M17) Effectivity, complexity and computational aspects of algebraic geometry (14Q20) Multilinear algebra, tensor calculus (15A69) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (18)

A Counterexample to Comon's Conjecture ⋮ Abelian tensors ⋮ On Comon's conjecture over arbitrary fields ⋮ An introduction to the computational complexity of matrix multiplication ⋮ Algebraic geometry and representation theory in the study of matrix multiplication complexity and other problems in theoretical computer science ⋮ Finite mixtures, projection pursuit and tensor rank: a triangulation ⋮ On the structure tensor of \(\mathfrak{sl}_n\) ⋮ Bad and good news for Strassen's laser method: border rank of \(\mathrm{Perm}_3\) and strict submultiplicativity ⋮ New lower bounds for matrix multiplication and ⋮ Plethysm and fast matrix multiplication ⋮ Unnamed Item ⋮ Real rank boundaries and loci of forms ⋮ Spaces of sums of powers and real rank boundaries ⋮ Examples of \(k\)-regular maps and interpolation spaces ⋮ Computing images of polynomial maps ⋮ Apolarity, border rank, and multigraded Hilbert scheme ⋮ Equivalent polyadic decompositions of matrix multiplication tensors ⋮ Rank decomposition and symmetric rank decomposition over arbitrary fields

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