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arXiv · 1706.05074

Polynomials and the exponent of matrix multiplication

Luca Chiantini·Jonathan D. Hauenstein·Christian Ikenmeyer·J. M. Landsberg·Giorgio Ottaviani
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Abstract

We define tensors, corresponding to cubic polynomials, which have the same exponent $\omega$ as the matrix multiplication tensor. In particular, we study the symmetrized matrix multiplication tensor $sM_n$ defined on an $n\times n$ matrix $A$ by $sM_n(A)=trace(A^3)$. The use of polynomials enables the introduction of additional techniques from algebraic geometry in the study of the matrix multiplication exponent $\omega$.

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Luca Chiantini, Jonathan D. Hauenstein, Christian Ikenmeyer, J. M. Landsberg, Giorgio Ottaviani. 2017-06-15. Polynomials and the exponent of matrix multiplication. https://doi.org/10.1112/blms.12147

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