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arXiv · 1301.0472

Introduction to the hyperdeterminant and to the rank of multidimensional matrices

Giorgio Ottaviani
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Abstract

This is an introduction to the hyperderminant, according to Gelfand, Kapranov and Zelevinsky. The "triangle inequality", characterizing the Segre varieties such that their dual variety is a hypersurface, is proved in a geometric way (Theorems 3.3 and 6.2). Significant emphasis is given to boundary format case, to pencil of quadrics and to the rank of multidimensional matrices. In the last section we propose three open problems.

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Giorgio Ottaviani. 2013-01-03. Introduction to the hyperdeterminant and to the rank of multidimensional matrices. https://arxiv.org/abs/1301.0472

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