Basis (linear algebra) - ordering of the vectors? Looking at Wikipedia Basis (linear algebra)), it seems that in English a basis is a set of vectors that may be ordered, with ordering not being mandatory. This creates issues when dealing with coordinates of vectors. In French a **"base"** is supposed to be ordered. **Do we have to mention an _ordered basi_ s to stipulate explicitly in English that the basis is ordered? Or does in practice a basis have implicitly an order?** _Note: this question hasthis one for background._

In my mind, a basis does not automatically come with an order (and indeed the order is usually superfluous). There are times when the order of the basis matters (Gram–Schmidt, for example), and in that case I'm used to either seeing the words "ordered basis" explicitly, or else the author sloppily assuming that the reader can figure out that an order is needed.