I read this stackexchange about whether to say “basis of” or “basis for”. Does the answer given there (that both are correct,

ofis newer andforis still more common) apply to mathematics as well?

**Answer**

The two forms are **completely interchangeable**. English in mathematical publications is “Global English”, and often written by non-native speakers who get the traditional grammar wrong, but it doesn’t matter because the meaning is carried by the mathematical symbols.

As I expect you know, *for* and *of* have directional connotations, with *for* meaning *towards* and *of* meaning *away from*. However, the association between a vector space and a basis works both ways.

That said, your reference to the basis and the vector space may be written in a directional context, e.g. with one step preceding another in your exposition. One form may sound more natural than the other.

Or you may have a personal preference based on how you see a basis being used in general, e.g. you find a basis because you intend to use it *for something*. However, this varies according to a person’s first language, which basically gets us back to Global English and the interchangeability of the two forms.

**Attribution***Source : Link , Question Author : Tomlish , Answer Author : Global Charm*