On Blocky Ranks Of Matrices

Daniel Avraham; Amir Yehudayoff

doi:https://doi.org/10.1007/s00037-024-00248-1

On Blocky Ranks Of Matrices

Daniel Avraham, Amir Yehudayoff

Mathematics

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

A matrix is blocky if it is a "blowup" of a permutation matrix. The blocky rank of a matrix M is the minimum number of blocky matrices that linearly span M. Hambardzumyan, Hatami and Hatami defined blocky rank and showed that it is connected to communication complexity and operator theory. We describe additional connections to circuit complexity and combinatorics, and we prove upper and lower bounds on blocky rank in various contexts.

Original language	English
Article number	2
Journal	Computational Complexity
Volume	33
Issue number	1
DOIs	https://doi.org/10.1007/s00037-024-00248-1
State	Published - Jun 2024

Keywords

68Q11
68R10
Communication complexity
fat matchings
matrix rank
threshold circuits

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Mathematics
Computational Theory and Mathematics
Computational Mathematics

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https://doi.org/10.1007/s00037-024-00248-1

Cite this

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N2 - A matrix is blocky if it is a "blowup" of a permutation matrix. The blocky rank of a matrix M is the minimum number of blocky matrices that linearly span M. Hambardzumyan, Hatami and Hatami defined blocky rank and showed that it is connected to communication complexity and operator theory. We describe additional connections to circuit complexity and combinatorics, and we prove upper and lower bounds on blocky rank in various contexts.

AB - A matrix is blocky if it is a "blowup" of a permutation matrix. The blocky rank of a matrix M is the minimum number of blocky matrices that linearly span M. Hambardzumyan, Hatami and Hatami defined blocky rank and showed that it is connected to communication complexity and operator theory. We describe additional connections to circuit complexity and combinatorics, and we prove upper and lower bounds on blocky rank in various contexts.

KW - 68Q11

KW - 68R10

KW - Communication complexity

KW - fat matchings

KW - matrix rank

KW - threshold circuits

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JF - Computational Complexity

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ER -

On Blocky Ranks Of Matrices

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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