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.
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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.
He not only explains how and why that is so, he also demonstrates linear algebra's nature through a wide variety of applications, covering vector spaces, Gaussian eliminations, eigenvalues and eigenvectors, determinants, calculating Jordan forms, normal linear spaces, inner product spaces and orthogonality, matrices, singular values and related inequalities, pseudoinverses, difference equations and differential operations, vector related functions, external problems, matrix values holomorphic functions, realization theory, eigenvalue locator problems, zero location problems, convexity and matrices with nonnegative spaces.