orthonormal basis

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• Orthonormal basis — In mathematics, particularly linear algebra, an orthonormal basis for inner product space V with finite dimension is a basis for V whose vectors are orthonormal.[1][2][3] For example, the standard basis for a Euclidean space Rn is an orthonormal… …   Wikipedia

• Basis (linear algebra) — Basis vector redirects here. For basis vector in the context of crystals, see crystal structure. For a more general concept in physics, see frame of reference. In linear algebra, a basis is a set of linearly independent vectors that, in a linear… …   Wikipedia

• Orthonormal function system — An orthonormal function system (ONS) is an orthonormal basis in a vector space of functions. See basis (linear algebra), Fourier analysis, square integrable, Hilbert space for more. Categories: Mathematics stubsLinear algebraFunctional analysis …   Wikipedia

• orthonormal — adjective Date: 1932 1. of real valued functions orthogonal with the integral of the square of each function over a specified interval equal to one 2. being or composed of orthogonal elements of unit length < orthonormal basis of a vector space > …   New Collegiate Dictionary

• orthonormal — ˌ adjective Etymology: orth + normal 1. of real valued functions : orthogonal with the integral of the square of each function over a specified interval equal to one 2. : being or composed of orthogonal elements of unit length orthonormal basis… …   Useful english dictionary

• Orthonormal — Als orthonormal (genauer: zueinander orthonormal) werden in der Mathematik Vektoren bezeichnet, die zueinander orthogonal sind und alle die Norm (anschaulich: Länge) eins besitzen. Eine Basis eines Vektorraums aus orthonormalen Vektoren bildet… …   Deutsch Wikipedia

• Orthonormal frame — In Riemannian geometry and relativity theory, an orthonormal frame is a tool for studying the structure of a differentiable manifold equipped with a metric. If M is a manifold equipped with a metric g, then an orthonormal frame at a point P of M… …   Wikipedia

• Basis function — In mathematics, particularly numerical analysis, a basis function is an element of the basis for a function space. The term is a degeneration of the term basis vector for a more general vector space; that is, each function in the function space… …   Wikipedia

• Standard basis — In mathematics, the standard basis (also called natural basis or canonical basis) of the n dimensional Euclidean space Rn is the basis obtained by taking the n basis vectors:{ e i : 1leq ileq n}where e i is the vector with a 1 in the ith… …   Wikipedia

• Change of basis — In linear algebra, change of basis refers to the conversion of vectors and linear transformations between matrix representations which have different bases. Contents 1 Expression of a basis 2 Change of basis for vectors 2.1 Tensor proof …   Wikipedia

• Schauder basis — In mathematics, a Schauder basis or countable basis is similar to the usual (Hamel) basis of a vector space; the difference is that Hamel bases use linear combinations that are finite sums, while for Schauder bases they may be infinite sums. This …   Wikipedia