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arXiv · 1205.0910

On projections of arbitrary lattices

Antonio Campello·João Strapasson·Sueli Costa
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Abstract

In this paper we prove that given any two point lattices $\Lambda_1 \subset \mathbb{R}^n$ and $ \Lambda_2 \subset \nobreak \mathbb{R}^{n-k}$, there is a set of $k$ vectors $\bm{v}_i \in \Lambda_1$ such that $\Lambda_2$ is, up to similarity, arbitrarily close to the projection of $\Lambda_1$ onto the orthogonal complement of the subspace spanned by $\bm{v}_1, \ldots, \bm{v}_k$. This result extends the main theorem of \cite{Sloane2} and has applications in communication theory.

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Antonio Campello, João Strapasson, Sueli Costa. 2012-05-04. On projections of arbitrary lattices. https://doi.org/10.1016/j.laa.2013.07.022 10.1016/j.laa.2013.07.022

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