Revision as of 21:20, 6 October 2007 by imported>Hendra I. Nurdin
In mathematics, an inner product space is a vector space that is endowed with an inner product. It is also a normed space since an inner product induces a norm on the vector space on which it is defined. A complete inner product space is called a Hilbert space.
Examples of inner product spaces
- The Euclidean space
endowed with the real inner product
for all
. This inner product induces the Euclidean norm 
- The space
of the equivalence class of all complex-valued Lebesque measurable scalar square integrable functions on
with the complex inner product
. Here a square integrable function is any function f satisfying
. The inner product induces the norm 
See also
Completeness
Banach space
Hilbert space