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.
- AMS subject classification (1980): 05B20
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Computational Mathematics