Definition:Inner Product Space

Definition
An inner product space is a vector space together with an associated inner product.

Also known as
It is also sometimes known as a pre-Hilbert space because by the Completion Theorem we can extend an inner product space to its completion, so it becomes a Hilbert space.

Also see

 * Definition:Inner Product


 * Definition:Semi-Inner Product Space
 * Definition:Hilbert Space


 * Norm satisfying Parallelogram Law induced by Inner Product: Corollary gives a complete classification of the normed vector spaces over $\R$ that can be identified with an inner product space. (with the identification from the "Notes" section)