inner product

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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.

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

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

dot product, scalar product

real, real number - any rational or irrational number

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References in periodicals archive ?

In [section]2 we explain the interpretation of the Hecke operators on [M.sub.3m]([GAMMA]) and the Petersson inner product on [S.sub.3]([GAMMA]) in terms of the pluricanonical forms.

Modular forms of weight 3m and elliptic modular surfaces

The inner product of incident wave [r.sub.s]'s unit vector and subreflector's unit normal vector is

A Ring-Focus Antenna with Splash Plate in Ka-Band

By a number of authors [1-4], it has been recommended to enhance the flexibility of the formalism by making use of an ad hoc, quantum-system-adapted physical inner product in H, that is, by an introduction of a nontrivial, stationary metric operator [THETA] [not equal to] [THETA](t).

Hermitian-Non-Hermitian Interfaces in Quantum Theory

In this section, we define a new inner product to determine the solution which satisfies the initial boundary value problem.

The Solution of Initial Boundary Value Problem with Time and Space-Fractional Diffusion Equation via a Novel Inner Product

These polynomials coincide with the orthogonal polynomials associated with the inner product defined in (6) and verify

Numerical Procedures for Random Differential Equations

Obviously, the Fock-Sobolev type space [F.sup.p.sub.[alpha]] equipped with the natural inner product defined by

Sarason's Conjecture of Toeplitz Operators on Fock-Sobolev Type Spaces

Functional Encryption for Inner Product. Although FE supports the computation of general circuits relying on a wide spectrum of assumptions, there are two major problems with the state-of-the-art general FE constructions.

Improved Construction for Inner Product Functional Encryption

Then for each block, a dissimilar dictionary is learned by using the inner product approach.

A novel hybrid method for robust infrared target detection

In Section 2, we introduce the concept of a matrix-valued inner product [<<x,x>>.sub.S] for block vectors with values in a *-algebra S [subset] [C.sup.s x s].

BLOCK KRYLOV SUBSPACE METHODS FOR FUNCTIONS OF MATRICES

Since cochains are column vectors, we use an inner product between two column vectors to represent the volume integration of their wedge product.

Electromagnetic Theory with Discrete Exterior Calculus

We will be able to use some specific mathematical tools as inner product.

Some Notes about the Continuous-in-Time Financial Model

A solution for this problem is provided by conformal geometric algebra (CGA), which can represent the geometries of Euclidean space effectively by the outer product, inner product, and geometric product.

Forward Displacement Analysis of a General 6-3 Stewart Platform Using Conformal Geometric Algebra

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