Inner product
From Conservapedia
In linear algebra, an inner product 
in a vector space 
is a function from 
to 
satisfying the following axioms for all vectors 
:[1]
, with 
if and only if 
,
(the inner product is commutative),
, and- for all
, 
.
One consequence of the inner product axioms is that the inner product is multilinear in both variables; that is:
The dot product in the Euclidean vector space 
is the best-known example of an inner product.
An inner product space is a vector space together with an inner product.
References
- ↑ Anton, Howard and Chris Rorres. Elementary Linear Algebra: Applications Version. 9th ed. N.p.:John Wiley & Sons, Inc., 2005. p. 296
