scalar product

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scalar product

n.
The numerical product of the lengths of two vectors and the cosine of the angle between them. Also called dot product, inner product.

scalar product

n
(Mathematics) the product of two vectors to form a scalar, whose value is the product of the magnitudes of the vectors and the cosine of the angle between them. Written: A·B or AB. Also called: dot product Compare vector product

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 scalar product - a real number (a scalar) that is the product of two vectorsreal, real number - any rational or irrational number
References in periodicals archive ?
The Gram determinant  (composed from pairwise scalar products of the current and voltage IV vectors) equals to square of the vectorial IP (8)
j] (j = 1,2) be separable Hilbert spaces with scalar products [<x, x>.
According to , CTC, describing the evolution of the trains of Manakov solitons must be modified by attaching the scalar products of the relevant polarization vectors to the exponential factors.
Also recently in , appropriate scalar products are studied, which can guide the choice of block-diagonal preconditioners for self-adjoint saddle-point problems.
He then moves to interval arithmetic, floating point arithmetic, implementation, hardware sorting for interval arithmetic, scalar products and complete arithmetic, principals of verified computing, and sample applications.
These scalar products are defined as in the complex case, but for some automatic restrictions imposed by the non commutativity of H: see the Appendix B for more details.
He covers implementations of arithmetic on computers (floating-point arithmetic and its implementation on a computer, hardware support for interval arithmetic and scalar products and complete arithmetic) and principles of verified computing including sample applications, including the extended interval Newton methods, verified solutions of systems of linear equations and multiple precision arithmetics.
The first one uses an index of confidence of the estimated orientation, and the second one the detection of minima of scalar products in a neighbourhood.
In this case [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], because according to the above, this inequality between the scalar products is valid and the coefficient -[epsilon] is positive.
The directional theory predicts that they will instead be based on the respective scalar products minus any penalty for parties outside the region of acceptability.

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