In
linear algebra, an
inner product space is a
vector space with an additional
structure called an
inner product. This additional structure associates each pair of vectors in the space with a
scalar quantity known as the inner product of the vectors. Inner products allow the rigorous introduction of intuitive geometrical notions such as the length of a vector or the
angle between two vectors. They also provide the means of defining
orthogonality between vectors (zero inner product). Inner product spaces generalize
Euclidean spaces (in which the inner product is the
dot product, also known as the scalar product) to vector spaces of any (possibly infinite)
dimension, and are studied in
functional analysis.