In linear algebra, an inner product in a vector space
is a function from
to
satisfying the following axioms for all vectors
:[1]
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.
Categories: [Mathematics]