Inner product space

:For the scalar product or dot product of spatial vectors see dot product

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

In mathematics, an inner product space is a vector space with additional structure, an inner product, scalar product or dot product, which allows us to introduce geometrical notions such as angles and lengths of vectors. Inner product spaces are generalizations of Euclidean space (with the dot product as the inner product) and are studied in functional analysis. An inner product space is also called a pre-Hilbert space, since its completion with respect to the metric induced by its inner product is a Hilbert space.

Related Topics:
Mathematics - Vector space - Angle - Length - Euclidean space - Dot product - Functional analysis - Completion - Metric - Induced - Hilbert space

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Inner product spaces were referred to as unitary spaces in earlier work, although this terminology is now rarely used.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~