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arXiv · 0808.2688

A simple estimation of the maximal rank of tensors with two slices by row and column operations, symmetrization and induction

Toshio Sakata·Toshio Sumi·Mitsuhiro Miyazaki
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Abstract

The determination of the maximal ranks of a set of a given type of tensors is a basic problem both in theory and application. In statistical applications, the maximal rank is related to the number of necessary parameters to be built in a tensor model. Based on this classical theorem by Bosch we will show the tight bound for 2 x n x n tensors by simple row and column operations, symmetrization and mathematical induction, which has been given by several authors based on eigenvalue theories.

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Toshio Sakata, Toshio Sumi, Mitsuhiro Miyazaki. 2008-08-20. A simple estimation of the maximal rank of tensors with two slices by row and column operations, symmetrization and induction. https://arxiv.org/abs/0808.2688

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