A lower bound for the border rank of a bilinear map

DOI10.1007/BF02579423zbMath0613.15024OpenAlexW2078979885MaRDI QIDQ1088760

Bernhard Griesser

Publication date: 1986

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02579423

zbMATH Keywords

computational complexitybilinear formslower boundsborder rank of tensors

Mathematics Subject Classification ID

Vector and tensor algebra, theory of invariants (15A72) Quadratic and bilinear forms, inner products (15A63) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items

The border rank of the multiplication of $2\times 2$ matrices is seven, On the Geometry of Border Rank Algorithms for n × 2 by 2 × 2 Matrix Multiplication, Nontriviality of equations and explicit tensors in \(\mathbb{C}^m \otimes \mathbb{C}^m \otimes \mathbb{C}^m\) of border rank at least \(2m - 2\)

Cites Work

• A note on border rank
• Rank and optimal computation of generic tensors
• Relations between exact and approximate bilinear algorithms. Applications
• On the optimal evaluation of a set of bilinear forms
• Tensor Rank and Border Rank of Band Toeplitz Matrices