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On the minimum number of Toeplitz factors of a matrix

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arxiv 2506.16432 v1 pith:E2QI3F65 submitted 2025-06-19 math.AC

Ignacio García-Marco , Irene Márquez-Corbella , Daniel Seco This is my paper
classification math.AC
keywords matricestoeplitzmatrixminimumnumbertimescomplexconjecture
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abstract

We disprove a conjecture by Ye and Lim, by showing that there are $3 \times 3$ complex matrices which can't be expressed as the product of two Toeplitz matrices of the same size. We also improve previous estimates by Ye and Lim on the minimum number of Toeplitz matrices needed to factor any $n \times n$ matrix, for low values of $n$.

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  1. Structured matrix factorization length

    math.AG 2026-06 unverdicted novelty 7.0 of 10

    Introduces structured matrix factorization length and X-factorization varieties, computes their dimensions for Toeplitz, Hankel, bidiagonal, tridiagonal, skew-symmetric, and companion matrices, and proposes displaceme...

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