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.

Question

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.

frethi38 · Accepted Answer

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                      ]

mravinjakag · Accepted Answer

The only other idea I have is: if A is unimodular then so is it&#039;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.

Unimodular Matrix is a matrix, which has integer entries and determinant of ∈

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