34.16 DiagonalizeMat

DiagonalizeMat( mat )

DiagonalizeMat transforms the integer matrix mat by multiplication with unimodular (i.e., determinant +1 or -1) integer matrices from the left and from the right into diagonal form (i.e., only diagonal entries are nonzero). Note that DiagonalizeMat changes mat and returns nothing. If there are several diagonal matrices to which mat is equivalent, it is not specified which one is computed, except that all zero entries on the diagonal are collected at the lower right end (see ElementaryDivisorsMat).

    gap> m := [ [ 0, -1, 1 ], [ -2, 0, -2 ], [ 2, -2, 4 ] ];;
    gap> DiagonalizeMat( m );  m;
    [ [ 1, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 0 ] ] 

Note that for large integer matrices DiagonalizeMat may take very long, because the entries may become very large during the computation, even if the final result only contains small integers.

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