  To represent real $m$-dimensional vectors, a positional vector system given
by a non-singular matrix $M \in \mathbb{Z}^{m \times m}$ and a digit set
$\mathcal{D} \subset \mathbb{Z}^m$ is used. If $m = 1$, the system coincides
with the well known numeration system used to represent real numbers. We study
some properties of the vector systems which are transformable from the case $m
= 1$ to higher dimensions. We focus on algorithm for parallel addition and on
systems allowing an eventually periodic representation of vectors with rational
coordinates.
