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.
Best Answer
You are correct. Any basis for a one dimensional inner product space is an orthogonal basis because the orthogonality condition is vacuously true, i.e. there are no pairs which must be orthogonal.