inner product space

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inner product space

[¦in·ər ′präd·əkt ‚spās]
(mathematics)
A vector space that has an inner product defined on it. Also known as generalized Euclidean space; Hermitian space; pre-Hilbert space.
References in periodicals archive ?
Physical Inner Products. The non-Hermiticity property of operators might cause complications in calculations.
Based on the independence of the random vector X11 and the random variables ([[xi].sub.j], p + 1 [less than or equal to] j [less than or equal to] n), the inner products in (56) are rearranged as
To guarantee correctness, our scheme requires that inner products be within a range of polynomial-size, which is consistent with other schemes in Table 1.
The following three combinations of S, [<<x,x>>.sub.S], and N, whose block inner products were first deduced in [22], satisfy the above definitions.
Taking the inner products <(1.1),2[phi]>, and <(1.2),2[psi]>, then summing up the resulting equalities and by the Neumann boundary conditions, we get
As a matter of fact, several inner products are to be defined when considering the inverse optimization problem.
Furthermore, matching the inner products of two Hermite polynomial tensors of equal rank, up to a given order N, will guarantee orthogonality of the Hermite polynomial tensors in the discrete space:
According to wavelet-Galerkin method, connection coefficients are the inner products of Daubechies scaling functions and their derivatives, because we are taking Daubechies scaling functions as a Galerkin basis.
According to equation (1), all of the inner products in Table 6 are shown as below:
This will be done by taking into account the weighting function in the inner products and by examining these ones case by case.
Sanz-Serna: On polynomials orthogonal with respect to certain Sobolev inner products, J.
The core of the book presents an axiomatic development of the most important elements of finite-dimensional linear algebra: vector spaces, linear operators, norms and inner products, and determinants and eigenvalues.