Characterization of Decomposition of Matrix Multiplication Tensors

Petr Tichavsky

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arXiv · 2104.05323

Characterization of Decomposition of Matrix Multiplication Tensors

Petr Tichavsky

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Abstract

In this paper, the canonical polyadic (CP) decomposition of tensors that corresponds to matrix multiplications is studied. Finding the rank of these tensors and computing the decompositions is a fundamental problem of algebraic complexity theory. In this paper, we characterize existing decompositions (found by any algorithm) by certain vectors called signature, and transform them in another decomposition which can be more suitable in practical algorithms. In particular, we present a novel decomposition of the tensor multiplication of matrices of the size 3x3 with 3x6 with rank 40.

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Petr Tichavsky. 2021-04-12. Characterization of Decomposition of Matrix Multiplication Tensors. https://arxiv.org/abs/2104.05323

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