### Abstract

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 language | English (US) |
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Pages (from-to) | 299-304 |

Number of pages | 6 |

Journal | Combinatorica |

Volume | 3 |

Issue number | 3-4 |

DOIs | |

State | Published - Sep 1983 |

### Keywords

- AMS subject classification (1980): 05B20

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Computational Mathematics

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## Cite this

Beck, J., & Spencer, J. (1983). Balancing matrices with line shifts.

*Combinatorica*,*3*(3-4), 299-304. https://doi.org/10.1007/BF02579185