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.