Appendix to ``Approximation of viscosity solutions of elliptic partial differential equations on minimal grids'', by M. Kocan: Approximation to orthogonal bases in \(\mathbb{R}^ n\) by orthogonal bases with integer coordinates (Q1907128)

Using ideas from the geometry of numbers and lattices, the author shows that an orthogonal base \(\underline\phi_1,\dots, \underline\phi_n\) for \(\mathbb{R}^n\), \(n\geq 4\), can be approximated by another orthogonal base \(\underline a_1,\dots, \underline a_n\) with integer components, in the sense that given \(N> 1\), then for each \(i= 1,\dots, n\), the angle between the vectors \(\underline\phi_i\) and \(\underline a_i\) is at most \(1/N\) and the norm of \(a_i\) is at most \(O(N^{2n- 4})\). This result is used in the paper by \textit{M. Kocan} [ibid. 72, No. 1, 73-92 (1995; reviewed above)].