Balancing matrices with line shifts

József Beck, Joel Spencer

Research output: Contribution to journalArticlepeer-review


We give a purely deterministic proof of the following theorem of J. Komlós and M. Sulyok. Let A=(a ij ), a ij =±1 be an n×n matrix. One can multiply some rows and columns by -1 such that the absolute value of the sum of the elements of the matrix is ≦2 if n is even and 1 if n is odd. Note that Komlós and Sulyok applied probabilistic ideas and so their method worked only for n>n 0.

Original languageEnglish (US)
Pages (from-to)299-304
Number of pages6
Issue number3-4
StatePublished - Sep 1983


  • AMS subject classification (1980): 05B20

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics


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