Wissenschaftliche Mitarbeiter

Philipp Reichenbach

Anschrift
Technische Universität Berlin
Institut für Mathematik
Sekretariat MA 3-2
Straße des 17. Juni 136
10623 Berlin

Büro
Raum MA 319 (3. OG)
Institut für Mathematik

Persönliche Homepage:
page.math.tu-berlin.de/~reichenb/

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0000-0002-5722-5505

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Beate Nießen
Raum MA 318
Tel.: +49 (0)30 314 - 25771

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reichenb@math.tu-berlin.de
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Tensor Rank and Complexity
Zitatschlüssel	OR-TensorRankAndComplexity
Autor	Giorgio Ottaviani and Philipp Reichenbach
Jahr	2020
Monat	4
Zusammenfassung	These lecture notes are intended as an introduction to several notions of tensor rank and their connections to the asymptotic complexity of matrix multiplication. The latter is studied with the exponent of matrix multiplication, which will be expressed in terms of tensor (border) rank, (border) symmetric rank and the asymptotic rank of certain tensors. We introduce the multilinear rank of a tensor as well, deal with the concept of tensor equivalence and study prehomogeneous vector spaces with the Castling transform. Moreover, we treat Apolarity Theory and use it to determine the symmetric rank (Waring rank) of some symmetric tensors.