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.

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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