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

the base space X {\displaystyle X} . It can be constructed by a method entirely analogous to that of the ordinary frame bundle. The orthonormal frame...

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

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...

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

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...

variety that satisfies an analog of compactness Complete orthonormal basis—see Orthonormal basis#Incomplete orthogonal sets Complete sequence, a type...

identified by crossed diagonals. If (i, j, k) is a positively oriented orthonormal basis, the basis vectors satisfy the following equalities i × j = k j...

the adjoint of a map is the transposed matrix only if the bases are orthonormal with respect to their bilinear forms. In this context, many authors however...

calculations. It is frequently the case that the vielbein coordinate system is orthonormal, as that is generally the easiest to use. Most tensors become simple...

unitary operators, and are described as unitary matrices relative to some orthonormal basis. Usually the computational basis is used, which unless comparing...

basis, cost of an asset Basis function Basis (linear algebra) Dual basis Orthonormal basis Schauder basis Basis (universal algebra) Basis of a matroid Generating...

transform Watershed transform (digital image processing) Wavelet transform (orthonormal) Y-Δ transform (electrical circuits) Linear transform List of Fourier-related...

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...

each with a unique eigenfunction, and that these eigenfunctions form an orthonormal basis of a certain Hilbert space of functions. This theory is important...

trihedron consists of a point P in Euclidean space, and three orthonormal vectors e1, e2, and e3 based at the point P. A moving trihedron is a trihedron whose...

A} ⁠ has orthonormal columns (then A ∗ A = A + A = I n {\displaystyle A^{*}A=A^{+}A=I_{n}} ),   or ⁠ B {\displaystyle B} ⁠ has orthonormal rows (then...

spherical harmonics form a complete set of orthogonal functions and thus an orthonormal basis, each function defined on the surface of a sphere can be written...

a vector space. An orthonormal frame of a vector space is an ordered basis consisting of orthogonal unit vectors (an orthonormal basis). An affine frame...

& Schwartz 1958, §IV.16). Among them is the theorem that, if A is an orthonormal set in a Hilbert space H, and x ∈ H , {\displaystyle x\in H,} then ⟨...

of a stochastic process: if the process is indexed over [a, b], any orthonormal basis of L2([a, b]) yields an expansion thereof in that form. The importance...

orthonormal bases (orthonormal n-frames). In other words, the space of orthonormal bases is like the orthogonal group, but without a choice of base point:...

exist orthonormal basis kets that span the entire Hilbert space. If the N-dimensional set { | ϕ i ⟩ } {\textstyle \{|\phi _{i}\rangle \}} is orthonormal, then...

the line. These directions (i.e., principal components) constitute an orthonormal basis in which different individual dimensions of the data are linearly...

{\displaystyle \rho } of a group G {\displaystyle G} , and let us work in an orthonormal basis. Thus, ρ {\displaystyle \rho } maps G {\displaystyle G} into the...

\mathbf {b} =[b_{1},b_{2},\cdots ,b_{n}]} , specified with respect to an orthonormal basis, is defined as: a ⋅ b = ∑ i = 1 n a i b i = a 1 b 1 + a 2 b 2 +...

state of a qubit can be represented by a linear superposition of its two orthonormal basis states (or basis vectors). These vectors are usually denoted as...

({\boldsymbol {\alpha }},{\boldsymbol {\beta }},\mathbf {u} )} a right-handed orthonormal basis, R u ( θ ) α = cos ⁡ ( θ ) α + sin ⁡ ( θ ) β , R u ( θ ) β = −...

k x ) {\displaystyle \psi _{k}(x)={\sqrt {2/\pi }}\sin(kx)} form an orthonormal basis. In particular, the (strong) limit of ψ k {\displaystyle \psi _{k}}...

formula for distance in terms of coordinates relies on the basis being orthonormal), but not the scalars themselves. Vectors themselves also do not change...