# Does a vector space with dimension 1 have an orthogonal basis?

Normally an orthogonal basis of a finite vector space is referred as a basis that contains many vectors, i.e. 2 or more.

Consider a vector space that its dimension is 1 - does it have an orthogonal basis?
Is it true to refer to all the bases of that vector space as "orthogonal"?

I didn't find a reference for that in Wikipedia.

• Indeed, that WP article on orthogonal basis is very stubby and does not discuss existence at all. However, the Gram-Schmidt process works in any finite dimensional inner product space, including dimension 1 (and even 0) – Hagen von Eitzen Feb 6 '15 at 19:23