From positional representation of numbers to positional representation of vectors
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To represent real m-dimensional vectors, a positional vector system given by a non-singular matrix M ∈ℤ^m × m and a digit set 𝒟⊂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.
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