Completion of a partial integral matrix to a unimodular 1 matrix
نویسنده
چکیده
7 We first characterize submatrices of a unimodular integral matrix. We then prove that if n entries of an 8 n× n partial integral matrix are prescribed and these n entries do not constitute a row or a column, then this 9 matrix can be completed to a unimodular matrix. Consequently an n× n partial integral matrix with n− 1 10 prescribed entries can always be completed to a unimodular matrix. 11 © 2005 Published by Elsevier Inc. 12 AMS classification: 15A36; 11C20 13
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