# Orthogonal

From AMS Glossary

## orthogonal

- Originally, at right angles; later generalized to mean the vanishing of a sum (or integral) of products.

The cosine of the angle between two vectors,**V**_{1}and**V**_{2}with respective components, (*x*_{1},*y*_{1},*z*_{1}) and (*x*_{2},*y*_{2},*z*_{2}), is proportional to the sum of products,*x*_{1}*x*_{2}+*y*_{1}*y*_{2}+*z*_{1}*z*_{2}. Hence, if the vectors are perpendicular, the latter sum equals zero. For this reason any two series of numbers, (*x*_{1},*x*_{2}, · · ·,*x*_{n}) and (*y*_{1},*y*_{2}, · · ·,*y*_{n}) is said to be orthogonal if*See*orthogonal functions.

- On an ocean-wave refraction diagram, a ray drawn everywhere at right angles to wave crests.