The Hermite and Smith normal forms of integer matrices.

Greg Fee (CECM)

Monday Feburary 2nd, 2004, in K9509 at 3:30pm.





The Hermite normal form of an integer matrix is a canonical form
for integer matrices under integer row operations. The integer row
operations are adding an integer multiple of one row to another row,
swapping two rows, and multiplying a row by -1. The Hermite normal
form is an upper triangular matrix. The Smith normal form of an integer 
matrix is a canonical form for integer matrices under both integer row
and column operations.  The Smith normal form is a diagonal matrix.
We look at some algorithms for computing these normal forms and the
transformation matrices that perform the operation.