In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V {\displaystyle V} with finite dimension is a basis for...
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Frame bundle (redirect from Orthonormal frame bundle)
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...
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function by a certain orthonormal series generated by a wavelet. This article provides a formal, mathematical definition of an orthonormal wavelet and of the...
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Hilbert space (section Orthonormal bases)
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...
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Frame fields in general relativity (redirect from Orthonormal tetrad formalism)
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...
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generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any m × n {\displaystyle m\times n} matrix. It is related...
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variety that satisfies an analog of compactness Complete orthonormal basis—see Orthonormal basis#Incomplete orthogonal sets Complete sequence, a type...
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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...
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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...
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transform Watershed transform (digital image processing) Wavelet transform (orthonormal) Y-Δ transform (electrical circuits) Linear transform List of Fourier-related...
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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...
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unitary operators, and are described as unitary matrices relative to some orthonormal basis. Usually the computational basis is used, which unless comparing...
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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...
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each with a unique eigenfunction, and that these eigenfunctions form an orthonormal basis of a certain Hilbert space of functions. This theory is important...
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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...
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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...
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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:...
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formula for distance in terms of coordinates relies on the basis being orthonormal), but not the scalars themselves. Vectors themselves also do not change...
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basis, cost of an asset Basis function Basis (linear algebra) Dual basis Orthonormal basis Schauder basis Basis (universal algebra) Basis of a matroid Generating...
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\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 +...
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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...
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({\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 = −...
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representation theorem. In a finite-dimensional space with a chosen orthonormal basis, writing | ψ ⟩ {\displaystyle |\psi \rangle } as a column vector...
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exist orthonormal basis kets that span the entire Hilbert space. If the N-dimensional set { | ϕ i ⟩ } {\textstyle \{|\phi _{i}\rangle \}} is orthonormal, then...
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the line. These directions (i.e., principal components) constitute an orthonormal basis in which different individual dimensions of the data are linearly...
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as a coordinate transformation (importantly, a transformation of an orthonormal basis), because for any motion of a body there is an inverse transformation...
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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...
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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...
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space, and the elements of a spinor space are spinors. After choosing an orthonormal basis of Euclidean space, a representation of the Clifford algebra is...
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by the spectral theorem, it's always possible to diagonalize A in an orthonormal basis {qi}. The decomposition can be derived from the fundamental property...
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