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Balanced \(0,\pm 1\) matrices. I: Decomposition. (English) Zbl 1026.05016
Summary: A \(0\), \(\pm 1\) matrix is balanced if, in every square submatrix with two nonzero entries per row and column, the sum of the entries is a multiple of four. This paper extends the decomposition of balanced \(0\), \(1\) matrices obtained by M. Conforti, G. Cornuéjols and M. R. Rao [J. Comb. Theory, Ser. B 77, 292-406 (1999; Zbl 1023.05025)] to the class of balanced \(0\), \(\pm 1\) matrices. As a consequence, we obtain a polynomial time algorithm for recognizing balanced \(0\), \(\pm 1\) matrices.

MSC:
05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
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