WordNet (r) 3.0 (2006):

inner product
    n 1: a real number (a scalar) that is the product of two vectors
         [syn: scalar product, inner product, dot product]

The Free On-line Dictionary of Computing (30 December 2018):

inner product

    In linear algebra, any linear map from a
   vector space to its dual defines a product on the vector
   space: for u, v in V and linear g: V -> V' we have gu in V' so
   (gu): V -> scalars, whence (gu)(v) is a scalar, known as the
   inner product of u and v under g.  If the value of this scalar
   is unchanged under interchange of u and v (i.e. (gu)(v) =
   (gv)(u)), we say the inner product, g, is symmetric.
   Attention is seldom paid to any other kind of inner product.

   An inner product, g: V -> V', is said to be positive definite
   iff, for all non-zero v in V, (gv)v > 0; likewise negative
   definite iff all such (gv)v < 0; positive semi-definite or
   non-negative definite iff all such (gv)v >= 0; negative
   semi-definite or non-positive definite iff all such (gv)v <=
   0.  Outside relativity, attention is seldom paid to any but
   positive definite inner products.

   Where only one inner product enters into discussion, it is
   generally elided in favour of some piece of syntactic sugar,
   like a big dot between the two vectors, and practitioners
   don't take much effort to distinguish between vectors and
   their duals.

   (1997-03-16)