What question did this study set out to answer?

The aim is to establish a lower bound for the border rank of the matrix multiplication tensor.

January 30, 2017International Mathematics Research NoticesOpen Access

A 2n²-log₂(n)-1 lower bound for the border rank of matrix multiplication

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The aim is to establish a lower bound for the border rank of the matrix multiplication tensor.
Employed the border substitution method for analysis.
Utilized Koszul flattenings to derive the lower bound.
The established lower bound is $2n^2 - \log_2(n) - 1$.

Implication

Randomized trial establishes a lower bound for the border rank of matrix multiplication tensors, suggesting new mathematical insights.

Abstract

Let M n C n 2 C n 2 C n 2 denote the matrix multiplication tensor for n n matrices. We use the border substitution method [2, 3, 6] combined with Koszul flattenings

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Cite This Study

Landsberg et al. (2017) studied this question.

synapsesocial.com/papers/69dba65af7e0c66ced835dd2 https://doi.org/10.1093/imrn/rnx025

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Implication

Randomized trial establishes a lower bound for the border rank of matrix multiplication tensors, suggesting new mathematical insights.

Abstract

Let M n C n 2 C n 2 C n 2 denote the matrix multiplication tensor for n n matrices. We use the border substitution method [2, 3, 6] combined with Koszul flattenings

A 2n²-log₂(n)-1 lower bound for the border rank of matrix multiplication

Key Points

Implication

Abstract

Discussion

Cite This Study

A 2n²-log₂(n)-1 lower bound for the border rank of matrix multiplication

Key Points

Implication

Abstract

Discussion

Cite This Study

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