On Blocky Ranks Of Matrices

被引：0
|
作者：
Avraham, Daniel [1 ]
Yehudayoff, Amir [1 ,2 ]
机构：
[1] Technion IIT, Dept Math, Hefa, Israel
[2] Univ Copenhagen, Dept Comp Sci, Copenhagen, Denmark
来源：
COMPUTATIONAL COMPLEXITY | 2024年 / 33卷 / 01期
关键词：
Communication complexity; matrix rank; threshold circuits; fat matchings; THRESHOLD CIRCUITS; GRAPH; DEPTH-2; EDGES;
D O I：
10.1007/s00037-024-00248-1
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
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.
引用
收藏
页数：18
相关论文
共 50 条
  • [11] RANKS OF MATRICES AND FAMILIES OF CONES
    HOFFMAN, AJ
    TRANSACTIONS OF THE NEW YORK ACADEMY OF SCIENCES, 1967, 29 (04): : 375 - &
  • [12] Counting problems and ranks of matrices
    Matsuki, Norichika
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 465 : 104 - 106
  • [13] On Ranks of Matrices Associated with Trees
    Guantao Chen
    Frank J. Hall
    Zhongshan Li
    Bing Wei
    Graphs and Combinatorics, 2003, 19 : 323 - 334
  • [14] Extreme Ranks for Block Matrices
    Zhang, Fengxia
    Zhao, Jianli
    Zhao, Linlin
    ADVANCES IN MATRIX THEORY AND ITS APPLICATIONS, VOL 1: PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON MATRIX THEORY AND ITS APPLICATIONS, 2008, : 409 - 412
  • [15] On ranks of matrices associated with trees
    Chen, GT
    Hall, FJ
    Li, ZS
    Wei, B
    GRAPHS AND COMBINATORICS, 2003, 19 (03) : 323 - 334
  • [16] On the Kapranov ranks of tropical matrices
    Shitov, Yaroslav
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 436 (09) : 3247 - 3253
  • [17] Minimal Ranks of Pattern Matrices
    Xu, Chang-Qing
    Zhang, Ju-Li
    ADVANCES IN MATRIX THEORY AND ITS APPLICATIONS, VOL II: PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON MATRIX THEORY AND ITS APPLICATIONS, 2008, : 367 - 370
  • [18] TERM RANKS AND PERMANENTS OF NONEGATIVE MATRICES
    JURKAT, WB
    RYSER, HJ
    JOURNAL OF ALGEBRA, 1967, 5 (03) : 342 - &
  • [19] MIXED SUBDIVISIONS AND RANKS OF TROPICAL MATRICES
    Shitov, Yaroslav
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 142 (01) : 15 - 19
  • [20] Resilience of ranks of higher inclusion matrices
    Plaza, Rafael
    Xiang, Qing
    JOURNAL OF ALGEBRAIC COMBINATORICS, 2018, 48 (01) : 31 - 50
12345