guarantees that every vector space admits an orthonormal basis. This is possibly the most significant use of orthonormality, as this fact permits operators on inner-product...

In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V {\displaystyle V} with finite dimension is a basis for...

In Riemannian geometry and relativity theory, an orthonormal frame is a tool for studying the structure of a differentiable manifold equipped with a metric...

function by a certain orthonormal series generated by a wavelet. This article provides a formal, mathematical definition of an orthonormal wavelet and of the...

algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. One way to express this is...

the first two conditions basis is called an orthonormal system or an orthonormal set (or an orthonormal sequence if B is countable). Such a system is...

possible to talk about the set of all orthonormal frames for Ex. An orthonormal frame for Ex is an ordered orthonormal basis for Ex, or, equivalently, a linear...

These matrices are traceless, Hermitian, and obey the extra trace orthonormality relation, so they can generate unitary matrix group elements of SU(3)...

product space has an orthonormal basis. The two previous theorems raise the question of whether all inner product spaces have an orthonormal basis. The answer...

relativity (also called a tetrad or vierbein) is a set of four pointwise-orthonormal vector fields, one timelike and three spacelike, defined on a Lorentzian...

an element x {\displaystyle x} in a Hilbert space with respect to an orthonormal sequence. The inequality was derived by F.W. Bessel in 1828. Let H {\displaystyle...

An orthonormal function system (ONS) is an orthonormal basis in a vector space of functions. Melzak, Z. A. (2012), Companion to Concrete Mathematics,...

forms an orthonormal basis in the simplex. The values x i ∗ , i = 1 , 2 , … , D − 1 {\displaystyle x_{i}^{*},i=1,2,\ldots ,D-1} are the (orthonormal and Cartesian)...

dimension n. Conversely, the choice of a point called the origin and an orthonormal basis of the space of translations is equivalent with defining an isomorphism...

An orthogonal wavelet is a wavelet whose associated wavelet transform is orthogonal. That is, the inverse wavelet transform is the adjoint of the wavelet...

each other. By technical definition, it is a method of constructing an orthonormal basis from a set of vectors in an inner product space, most commonly...

maximally entangled (according to the entropy of entanglement) and form an orthonormal basis (linear algebra) of the Hilbert space of the two qubits. They play...

{\displaystyle U^{-1}=U^{*}} . The columns of U {\displaystyle U} form an orthonormal basis of C n {\displaystyle \mathbb {C} ^{n}} with respect to the usual...

generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any m × n {\displaystyle m\times n} matrix. It is related...

Orthogonal trajectory Orthogonalization Gram–Schmidt process Orthonormal basis Orthonormality Pan-orthogonality occurs in coquaternions Up tack J.A. Wheeler;...

Walsh functions. These are binary square waves that form a complete orthonormal set. The data signal is also binary and the time multiplication is achieved...

Hilbert space. See Spectral theorem for more details. Also called "Dirac orthonormality", according to Griffiths, David J. Introduction to Quantum Mechanics...

factorization, is a decomposition of a matrix A into a product A = QR of an orthonormal matrix Q and an upper triangular matrix R. QR decomposition is often...

known as tesseral spherical harmonics. These functions have the same orthonormality properties as the complex ones Y ℓ m : S 2 → C {\displaystyle Y_{\ell...

respect to this inner product. Usually the sequence is required to be orthonormal, namely, ⟨ P n , P n ⟩ = 1 , {\displaystyle \langle P_{n},P_{n}\rangle...

called an orthonormal basis. For a given inertial frame, an orthonormal basis in space, combined with the unit time vector, forms an orthonormal basis in...

Szegő kernel plays the role of the Cauchy integral. Given a complete orthonormal basis set of functions {φn} in a separable Hilbert space, for example...

In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed...

entries whose columns and rows are orthogonal unit vectors (that is, orthonormal vectors). Equivalently, a matrix A is orthogonal if its transpose is...

vectors of an orthogonal basis are normalized, the resulting basis is an orthonormal basis. Any orthogonal basis can be used to define a system of orthogonal...