Balanced 0, ±1 Matrices I. Decomposition

A 0, ±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 Conforti, Cornuéjols, and Rao (1999, J. Combin. Theory Ser. B77, 292–406) to the class of balanced 0, ±1 matrices. As a consequence, we obtain a polynomial time algorithm for recognizing balanced 0, ±1 matrices.