On orthogonal bases for rational lattices (Q1972179)

Let \(V\) be a Euclidean space and let \(e_1,\ldots,e_m\) be an orthonormal basis of \(V\). A lattice \(L\subset V\) is said to be rational (integer) if every vector \(v\in L\) has rational (integer) coordinates. In the article it is proven that a rational lattice \(L\) has an orthogonal basis if and only if some integer lattice \(L'\) has. A sufficient condition is also found for an integer lattice \(L\) to have an orthogonal basis.