scalar product

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

American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

scalar product

(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

Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

in′ner prod′uct

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.

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Noun

scalar product - a real number (a scalar) that is the product of two vectors

dot product, inner product

real, real number - any rational or irrational number

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References in periodicals archive

The general procedure they present associates to every strongly local vertex operator algebra V a conformal net AV acting on the Hilbert space completion of V, and prove that the isomorphism class of AV does not depend on the choice of the scalar product on V.

From Vertex Operator Algebras to Conformal Nets and Back

The canonical scalar product in [R.sup.n] is defined by x [mathematical expression not reproducible] y= <x,y>:=[x.sub.i][y.sub.i] (using the Einstein sum convention) for every x,y [member of] [R.sup.n].

Tensor series expansion of a spherical function for the use in constitutive theory of materials containing orientable particles

Suppose that we have a B-orthogonal projector P onto the subspace X = span(X) at hand, meaning its image and null space are orthogonal to each other with respect to the scalar product induced by B; see below for details.

CONVERGENCE OF INTEGRATION-BASED METHODS FOR THE SOLUTION OF STANDARD AND GENERALIZED HERMITIAN EIGENVALUE PROBLEMS

where D(v) : D(u) denotes the scalar product of tensors D(v) and D(u):

On Flows of Bingham-Type Fluids with Threshold Slippage

Let H be a Hilbert space over R with a scalar product (*,*), D be a symmetric unit-normed dictionary in H (i.e., [bar.span D] = H, all elements in D have a unit norm, and if g [member of] D, then -g also belongs to D).

Greedy Expansions with Prescribed Coefficients in Hilbert Spaces

Vectors are orthogonal if their scalar product is zero:

The development of the theory of instantaneous power of three-phase network in terms of network centrism

The G-invariant metric g induces a scalar product <*, *> on m which is Ad(K)-invariant.

Homogeneous Geodesies in Generalized Wallach Spaces

For simplicity, by k(t, s) f (s, x(s)) we mean the complex < k(t, s), f(s,u(s)) >, where < x, x > is the scalar product on the space E.

Existence and Ulam Stability Results for Quadratic Integral Equations

If Po is orthogonal projector on Toy w.r.t entropic scalar product (10), then vector projection (thermodynamic) of x is defined as:

Initially Approximated Quasi Equilibrium Manifold