# Orthogonormal and Basis Vectors

1. Mar 10, 2008

### pr0me7heu2

Would all bases be sets of orthogonal (but not necessarily orthonormal) vectors?

2. Mar 10, 2008

### morphism

No. Try to think of a basis for R^2 consisting of nonorthogonal vectors -- there are plenty.

3. Mar 10, 2008

### HallsofIvy

Staff Emeritus
For example, {$\vec{i}$, $\vec{i}+ \vec{j}$ } is a basis for R2 and they are not orthogonal (with the "usual" inner product). It happens to be easier to to find components in an orthonormal basis.

In any case, "orthogonal" as well as "orthonormal" depend upon an innerproduct defined on the vector space. Given any basis it is always possible to define an innerproduct in which that basis is orthonormal.