Completion of a partial integral matrix to a unimodular matrix |
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Authors: | Xingzhi Zhan |
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Institution: | Department of Mathematics, East China Normal University, Shanghai 200062, China |
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Abstract: | We first characterize submatrices of a unimodular integral matrix. We then prove that if n entries of an n × n partial integral matrix are prescribed and these n entries do not constitute a row or a column, then this matrix can be completed to a unimodular matrix. Consequently an n × n partial integral matrix with n − 1 prescribed entries can always be completed to a unimodular matrix. |
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Keywords: | 15A36 11C20 |
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