An Introduction to Algebraic Statistics with Tensors by Cristiano Bocci & Luca Chiantini

Author:Cristiano Bocci & Luca Chiantini
Language: eng
Format: epub
ISBN: 9783030246242
Publisher: Springer International Publishing

where indicates the times in which i occurs in the multi-index J.

With the notation just introduced, one can describe the multiplicity . Indeed a permutation changes the multi-index, unless it simply switches indices which are equal. Since the number of permutations over a set with m elements is m!, then one finds that

Proposition 7.4.2

Let G be a homogeneous polynomial of degree d in n variables, so that .

Then t(G) has rank 1 if and only if there exists a homogeneous linear polynomial , such that .

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