Hello all,

I have a singular square matrix E (12x12 with its rank of 10). I need to find 2 invertible matrices S and T such that S.E.T is a square diagonal matrix (in Smith Normal form). 

Using Maple with the following commands:
>Temp := SmithForm(E);
>Rank(Temp) 
Temp is a identity Matrix and Rank of (Temp)  is 12!!! or Rank of (S.E.T) = 12.

However, the determinant of E is less than 10^-29 and rank of E is 10.