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To represent real $m$-dimensional vectors, a positional vector system givenby 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 coincideswith the well known numeration system used to represent real numbers. We studysome properties of the vector systems which are transformable from the case $m= 1$ to higher dimensions. We focus on algorithm for parallel addition and onsystems allowing an eventually periodic representation of vectors with rationalcoordinates.

From positional representation of numbers to positional representation of vectors