Unimodular Matrix is a matrix, which has integer entries and determinant of &#x2208;<!-- ∈ -->

pokoljitef2 2022-06-07 Answered
Unimodular Matrix is a matrix, which has integer entries and determinant of { + 1 , 1 }. That means the matrix is invertible over the integers Z.
Given a unimodular matrix A for example:
[ 2 2 5 4 2 3 0 1 0 0 0 0 1 0 3 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ]
Need to convert to it to a matrix like this:
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
where * denotes possible nonzero entries.
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Answers (2)

frethi38
Answered 2022-06-08 Author has 16 answers
The inverse is:
[ 3 6 5 7 11 9 0 1 0 0 0 0 1 2 2 2 4 3 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ]
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mravinjakag
Answered 2022-06-09 Author has 4 answers
The only other idea I have is: if A is unimodular then so is it's inverse, so let M = A 1 M where M is unimodular of the form you want and chosen such that A 1 M has the desired first row.
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