From positional representation of numbers to positional representation of vectors
To represent real m-dimensional vectors, a positional vector system given by a non-singular matrix M ∈ ℤm×m and a digit set Ɗ ⊂ ℤm 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 t...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
CTU Central Library
2023-07-01
|
| Series: | Acta Polytechnica |
| Subjects: | |
| Online Access: | https://ojs.cvut.cz/ojs/index.php/ap/article/view/8536 |
| Summary: | To represent real m-dimensional vectors, a positional vector system given by a non-singular matrix M ∈ ℤm×m and a digit set Ɗ ⊂ ℤm 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 an algorithm for parallel addition and on systems allowing an eventually periodic representation of vectors with rational coordinates.
|
|---|---|
| ISSN: | 1805-2363 |