8 Inner product spaces

Welcome to the last chapter, where we discuss inner products. Technically, an

inner product is just a special case of a positive-definite symmetric bilinear or

hermitian form. However, they are usually much more interesting and useful.

Many familiar notions such as orthogonality only make sense when we have an

inner product.

In this chapter, we will adopt the convention that

F

always means either

R

or C, since working with other fields doesn’t make much sense here.