In this chapter, points and vectors are introduced. In spite of their strong relations, the difference between these concepts is emphasized. The distinction between them is sometimes not easy because both items are mostly described in the same way, namely by columns of coefficients. Indeed, it is often not necessary to know the real meaning of such columns, and they can be treated in the same way independently of their nature. Sometimes, however, their behaviour is different and their distinction is necessary for a real understanding of the description of crystallographic objects and to avoid mistakes.
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