# Inner Product

(1) In a vector space, an inner product is a way to multiply vectors together, with the result being a scalar. (2) In vector algebra, the term inner product is used as a synonym for dot product.

Inner product is a college-level concept that would be first encountered in a linear algebra course.

### Examples

Dot Product: | The dot product is particular product of two vectors which results in a scalar corresponding to the length of the projection of one vector onto the other. |

### Prerequisites

Vector: | (1) In vector algebra, a vector mathematical entity that has both magnitude (which can be zero) and direction. (2) In topology, a vector is an element of a vector space. |

Vector Space: | A vector space is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space. |