Hermite normal form
In linear algebra, the Hermite normal form is an analogue of reduced echelon form for matrices over the integers Z {\displaystyle \mathbb {Z} } . Just as reduced echelon form can be used to solve problems about the solution to the linear system A x = b {\displaystyle Ax=b} where x ∈ R n {\displaystyle x\in \mathbb {R} ^{n}} , the Hermite normal form can solve problems about the solution to the linear system A x = b {\displaystyle Ax=b} where this time x {\displaystyle x} is restricted to have integer coordinates only.