Vol. 16, No. 5, 2022

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On the geometry of geometric rank

Runshi Geng and Joseph M. Landsberg

Vol. 16 (2022), No. 5, 1141–1160
Abstract

We make a geometric study of the geometric rank of tensors recently introduced by Kopparty et al. Results include classification of tensors with degenerate geometric rank in 3 3 3, classification of tensors with geometric rank two, and showing that upper bounds on geometric rank imply lower bounds on tensor rank.

Keywords
geometric rank, matrix multiplication complexity, tensor rank, asymptotic rank, laser method
Mathematical Subject Classification
Primary: 14L30, 15A69, 68Q17
Milestones
Received: 8 December 2020
Revised: 5 August 2021
Accepted: 14 August 2021
Published: 16 August 2022
Authors
Runshi Geng
Department of Mathematics
Texas A&M University
College Station, TX
United States
Joseph M. Landsberg
Department of Mathematics
Texas A&M University
College Station, TX
United States