Appendix to "Approximation of viscosity solutions of elliptic partial differential equations on minimal grids", by M. Kocan: Approximation to orthogonal bases in ${\Bbb R}^n$ by orthogonal bases with integer coordinates

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In the Appendix it is shown that given $N>1$ , an orthogonal basis $\underline{\underline {\varphi_1}},\dots, \underline{\underline{\varphi_n}}$ of ${\Bbb R}^n$ where $n\ge4$ can be approximated by an orthogonal basis $\underline{\underline{a_1}},\dots, \underline{\underline{a_n}}$ with integer components such that the angle between $\underline{\underline{\varphi_i}}$ and $\underline{\underline{a_i}}$ is at most $1/N$ $(i=1,\dots,n)$ , and $\underline{\underline {a_1}},\dots, \underline{\underline{a_n}}$ have norms $\ll N^{2n-4}$ .