On the completion of a partial integral matrix to a unimodular matrix
Copyright policy )On the completion of a partial integral matrix to a unimodular matrix
A \textit{partial} \(n \times n\) integer matrix \(A\) is one in which some entries are indeterminates. A free diagonal for such a matrix is an \(n\)-tuple \(a_{1,\sigma(1)},\dots, a_{n,\sigma(n)}\) for a permutation \(\sigma\). The author shows that if \(A\) has a free diagonal, then there is an evaluation of the indeterminate entries that gives a unimodular matrix. Further, a partial matrix with \(2n-3\) prescribed entries so that any \(n\) do not constitute a row or column can also be completed to a unimodular matrix.
- East China Normal University China (People's Republic of)
Partial integral matrix, Numerical Analysis, Algebra and Number Theory, completion of matrix, partial integer matrix, Inverse problems in linear algebra, Matrices, determinants in number theory, Matrices of integers, Unimodular matrix, diagonal of matrix, Diagonal of matrix, unimodular matrix, Discrete Mathematics and Combinatorics, Geometry and Topology, Completion of matrix
Partial integral matrix, Numerical Analysis, Algebra and Number Theory, completion of matrix, partial integer matrix, Inverse problems in linear algebra, Matrices, determinants in number theory, Matrices of integers, Unimodular matrix, diagonal of matrix, Diagonal of matrix, unimodular matrix, Discrete Mathematics and Combinatorics, Geometry and Topology, Completion of matrix
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