Balancing matrices with line shifts
The authors give a deterministic proof [not a probabilistic one as in the original paper written by \textit{J. Komlós} and \textit{M. Suliok}, Comb. Theory Appl., Colloquia Math. Soc. János Bolyai 4, 721-728 (1970; Zbl 0216.020)] of the following theorem: If \(A=(a_{ij})\), with \(a_{ij}=\pm 1\) is a \(n\times n\) matrix, then it is possible to multiply some rows and columns by -1 such that the absolute value of the sum of the elements of the matrix is \(\leq 2\), if n is even and 1 if n is odd.
scientific article; zbMATH DE number 3861175