# 14: Orthonormal Bases and Complements

You may have noticed that we have only rarely used the dot product. That is because many of the results we have obtained do not require a preferred notion of lengths of vectors. Once a dot or inner product is available, lengths of and angles between vectors can be measured--very powerful machinery and results are available in this case.

### Contributor

David Cherney, Tom Denton, and Andrew Waldron (UC Davis)