# Inner product

### From Conservapedia

In linear algebra, an **inner product** in a vector space *V* 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