2021
DOI: 10.48550/arxiv.2104.05323
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Characterization of Decomposition of Matrix Multiplication Tensors

Petr Tichavsky

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 … Show more

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