# inner product

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## in′ner prod′uct

n.
the quantity obtained by multiplying the corresponding coordinates of each of two vectors and adding the products, equal to the product of the magnitudes of the vectors and the cosine of the angle between them. Also called dot product, scalar product.
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 inner product - a real number (a scalar) that is the product of two vectorsreal, real number - any rational or irrational number
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Let V be a real inner product space. Then the norm of the Einstein addition of two elements is given by the equation
As we can see in the fourth section, the Levinson Popoviciu inequality remains valid on the inner product spaces, under its original hypothesis or Mercer results hypothesis.
The commentary on Hilbert space entertains numerous illustrations of the inner product spaces wherein the metric produced by the inner product profits a complete metric space.
All the above arguments reveal that the space [H.sup.mxn] over field R with the inner product defined in (3) is an inner product space.
Pinsker (16) characterized orthogonally additive functionals on an inner product space when the orthogonality is the ordinary one in such spaces.
Let [P.sub.f] (N) be the family of finite parts of the natural number set N, [S.sub.+] (R) the cone of nonnegative real sequences and for a given inner product space (H; <[dot], [dot]>) over the real or complex number field K, S (H) the linear space of all sequences of vectors from H, i.e.,
Calculation of Jordan forms is followed by normed linear spaces, inner product spaces, orthogonality, and symmetric, Hermitian, and normal matrices.

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