Smith normal form

For every integer matrix

A

, there are unimodular matrices

U, V

such that

U A V = diag (d_{1}, \dots, d_{r}, 0, \dots, 0), d_{1} ∣ d_{2} ∣ \dots ∣ d_{r} .

The positive diagonal entries are unique. Their products

d_{1} \dots d_{k}

are the greatest common divisors of the

k

-rowed minors.

 Ancestors (4)