In this thesis we work on problems related to tensor decomposition from a geometrical perspective. In the first part of the thesis we focus on the identifiability problem, which amounts to understand in how many ways a tensor can be decomposed as a minimal sum of elementary tensors. In particular we completely classify the identifiability of any tensor up to rank 3. In the second part of the thesis we continue to work with specific elementsand we introduce the notion of r-thTerracini locus of a Segre variety. This is the locus containing all points for which the differential of the map between the r-th abstarct secant variety and the r-th secant variety of a Segre variety drops rank. We completely determine the r-th Terracini locus of any Segre variety in the case of r = 2, 3.

Identifiability of small rank tensors and related problems / Santarsiero, Pierpaola. - (2022 Apr 01), pp. 1-109. [10.15168/11572_335243]

Identifiability of small rank tensors and related problems

Santarsiero, Pierpaola
2022-04-01

Abstract

In this thesis we work on problems related to tensor decomposition from a geometrical perspective. In the first part of the thesis we focus on the identifiability problem, which amounts to understand in how many ways a tensor can be decomposed as a minimal sum of elementary tensors. In particular we completely classify the identifiability of any tensor up to rank 3. In the second part of the thesis we continue to work with specific elementsand we introduce the notion of r-thTerracini locus of a Segre variety. This is the locus containing all points for which the differential of the map between the r-th abstarct secant variety and the r-th secant variety of a Segre variety drops rank. We completely determine the r-th Terracini locus of any Segre variety in the case of r = 2, 3.
XXXIV
2019-2020
Matematica (29/10/12-)
Mathematics
Bernardi, Alessandra
Ballico, Edoardo
no
Inglese
Settore MAT/02 - Algebra
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/335243
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