Source : WordNet®

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

Source : Free On-Line Dictionary of Computing

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)