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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Applications for Sequences of Vectors in Inner Product Spaces
The topics include linear transformations, normed and inner product spaces, sesquilinear forms and unitary geometry, linear groups and groups of isometries, and applications of linear algebra.
Among his topics are coordinates, the structure of a linear transformation, real and complex inner product spaces, and matrix groups as Lie groups.
After transitioning from solving systems of two linear equations to solving general systems, this textbook introduces the algebraic properties of matrix operations, determinants, vector spaces, eigenvalues, eigenvectors, linear transformations, inner product spaces, numerical techniques, and linear programming.
Their topics reflect the preferences in their own research over the past decade: discrete inequalities, integral inequalities for convex functions, Ostrowski and trapezoid type inequalities, Gruss type inequalities and related results, inequalities in inner product spaces, and inequalities in normed linear spaces and for functionals.
Moore (computer and information science, Ohio State U.) and Cloud (electrical and computer engineering, Lawrence Technological U.) offer more than 100 exercise while covering linear spaces, topological spaces, metric spaces, normed linear spaces and Banach spaces, inner product spaces and Hilbert spaces, linear functionals, types of convergence in function space, reproducing kernel Hilbert spaces, order relations in function spaces, operators in function space, completely continuous operators, approximation methods for linear operator equations, interval methods for operator equations, contraction mappings and iterative methods, Newton's method in Banach spaces, variants of Newton's methods, and homotopy and continuation methods and a hybrid method for a free-boundary problem.
Chapters are presented on vector spaces, linear transformations, polynomials, theory of a single line operator, inner product spaces, linear operators on inner product spaces, trace and determinant of a linear operator, bilinear maps and forms, and tensor products.