I need a reference for the result of Hermite Normal Form of a matrix. I would prefer one which states the result in the following form:
the span of $ k $ $ \mathbb{Z} $-linearly independent vectors inside a free $ \mathbb{Z} $-module of rank $ n $, can be "represented" as matrix consisting of an upper triangular $ k \times k $ matrix, above a block of $ ( n - k ) \times k $ zero matrix.