A forma normal de Hermite

The Hermite normal form is similar of reduced echelon form for matrices with integer entries. In this article some results on this topic are presented, among which we highlight the existence and uniqueness Theorem, which states that every matrix is row equivalent to one, and only one, matrix in the Hermite normal form. An algorithm for computing the Hermite normal form of a matrix by the elementary unimodular operations is also given. Finally, some concepts and preliminary results on lattices are presented, including three problems that are answered using the Hermite normal form, namely, the problem of finding a basis of a lattice and the problems of equality and union of lattices.