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Longer titles found: Infinitesimal rotation matrix (view)

searching for Rotation matrix 50 found (158 total)

Rotations in 4-dimensional Euclidean space (5,712 words) [view diff] exact match in snippet view article find links to article

unit Euclidean norm as a 16D vector if and only if A is indeed a 4D rotation matrix. In this case there exist real numbers a, b, c, d and p, q, r, s such

Product of exponentials formula (1,116 words) [view diff] exact match in snippet view article find links to article

this configuration. It is an affine transform consisting of the 3x3 rotation matrix R and the 1x3 translation vector p. The matrix is augmented to create

Liouville's theorem (conformal mappings) (758 words) [view diff] exact match in snippet view article

}}{|x-a|}}\right),} where a, b are vectors in Rn, α is a scalar, A is a rotation matrix, ε = 0 or 2, and the matrix in parentheses is I or a Householder matrix

Jacobi eigenvalue algorithm (3,928 words) [view diff] exact match in snippet view article find links to article

and G = G ( i , j , θ ) {\displaystyle G=G(i,j,\theta )} be a Givens rotation matrix. Then: S ′ = G S G ⊤ {\displaystyle S'=GSG^{\top }\,} is symmetric

Cayley transform (2,248 words) [view diff] exact match in snippet view article find links to article

&-\sin \theta \\\sin \theta &\cos \theta \end{bmatrix}}.} The 180° rotation matrix, −I, is excluded, though it is the limit as tan θ⁄2 goes to infinity

Chrominance (651 words) [view diff] exact match in snippet view article find links to article

via the JPEG standard, the RGB color space is first converted (by a rotation matrix) to a YCbCr color space, because the three components in that space

Equinox (celestial coordinates) (1,749 words) [view diff] exact match in snippet view article

ISBN 978-0-7503-0886-1. Hilton, J. L.; Hohenkerk, C. Y. (2004). "Rotation matrix from the mean dynamical equator and equinox at J2000.0 to the ICRS"

Conjugate transpose (1,724 words) [view diff] exact match in snippet view article find links to article

representing complex numbers e i θ {\displaystyle e^{i\theta }} as the rotation matrix, that is, e i θ = ( cos ⁡ θ − sin ⁡ θ sin ⁡ θ cos ⁡ θ ) = cos ⁡ θ (

QR decomposition (4,633 words) [view diff] exact match in snippet view article find links to article

1&4\\6&167&-68\\-4&24&-41\end{bmatrix}}.} First, we need to form a rotation matrix that will zero the lowermost left element, a 31 = − 4 {\displaystyle

Generalized minimal residual method (3,328 words) [view diff] exact match in snippet view article find links to article

arnoldi(A, Q, k); % eliminate the last element in H ith row and update the rotation matrix [H(1:k+1, k), cs(k), sn(k)] = apply_givens_rotation(H(1:k+1,k), cs

Geometry processing (4,198 words) [view diff] exact match in snippet view article find links to article

X} onto surface Y {\displaystyle Y} , we want to find the optimal rotation matrix R {\displaystyle R} and translation vector t {\displaystyle t} that

Joint Approximation Diagonalization of Eigen-matrices (349 words) [view diff] exact match in snippet view article find links to article

optimizing a contrast function to obtain a m × m {\displaystyle m\times m} rotation matrix O {\displaystyle O} to estimate the source components given by the

Ammann–Beenker tiling (1,504 words) [view diff] exact match in snippet view article find links to article

corresponding to an eightfold rotational symmetry of the tesseract. A rotation matrix representing this symmetry is: A = [ 0 0 0 − 1 1 0 0 0 0 − 1 0 0 0

Precession (2,683 words) [view diff] exact match in snippet view article find links to article

evolution of the object's orientation, represented (for example) by a rotation matrix R that transforms internal to external coordinates, may be numerically

Degrees of freedom (mechanics) (2,165 words) [view diff] exact match in snippet view article

[T] = [A, d], where d is an n-dimensional translation and A is an n × n rotation matrix, which has n translational degrees of freedom and n(n − 1)/2 rotational

Screw theory (4,394 words) [view diff] exact match in snippet view article find links to article

parameterized set of spatial displacements, D(t)=([A(t)],d(t)), where [A] is a rotation matrix and d is a translation vector. This causes a point p that is fixed

Maximal torus (1,734 words) [view diff] exact match in snippet view article find links to article

{\displaystyle 2\times 2} diagonal blocks, where each diagonal block is a rotation matrix. This is also a maximal torus in the group SO(2n+1) where the action

Constraint (computational chemistry) (4,518 words) [view diff] exact match in snippet view article

then corrected by directly calculating and applying the rigid body rotation matrix that satisfies: L rigid ( t + Δ t 2 ) = L nonrigid ( t + Δ t 2 ) {\displaystyle

Armadillo (C++ library) (614 words) [view diff] exact match in snippet view article

particle // | arma::vec Pos = {{0}, // | (0,1) {1}}; // +---x--> // Rotation matrix double phi = -3.1416/2; arma::mat RotM = {{+cos(phi), -sin(phi)}, {+sin(phi)

Discrete Chebyshev polynomials (1,207 words) [view diff] exact match in snippet view article find links to article

polynomials turn out to be the eigenvectors of the absolute square of the rotation matrix (the Wigner D-matrix). The associated eigenvalue is the Legendre polynomial

Image rectification (1,764 words) [view diff] exact match in snippet view article find links to article

reprojection process. In this example, we simply define H' using the rotation matrix R and initial projective transformation H as H ′ = H R T {\displaystyle

ICtCp (1,869 words) [view diff] exact match in snippet view article find links to article

is also considers S (blue cone) for intensity, but ICTCP has also Rotation matrix (to align skin tones) and Scalar matrix (scaled to fit the full BT

Triad method (963 words) [view diff] exact match in snippet view article find links to article

for i = 1 , 2 {\displaystyle i=1,2} , where A {\displaystyle A} is a rotation matrix (sometimes also known as a proper orthogonal matrix, i.e., A T A =

USA Memory Championship (1,254 words) [view diff] case mismatch in snippet view article find links to article

events from Lumosity have typically been Memory Match Overdrive and Rotation Matrix, while the events from Memory League have been Images, Names, and Numbers

Burmester's theory (1,877 words) [view diff] exact match in snippet view article find links to article

transformations [Ti] = [Ai, di], i = 1, ..., 5, where [A] is a 2×2 rotation matrix and d is a 2×1 translation vector, that define task positions of a

Schur–Horn theorem (2,888 words) [view diff] exact match in snippet view article find links to article

9–20. Horn, Alfred, Doubly stochastic matrices and the diagonal of a rotation matrix, American Journal of Mathematics 76 (1954), 620–630. Kadison, R. V

Harris affine region detector (7,003 words) [view diff] exact match in snippet view article find links to article

region into isotropic regions that are related simply through a pure rotation matrix R {\displaystyle R} . These new isotropic regions can be thought of

Tangloids (1,790 words) [view diff] exact match in snippet view article find links to article

v_{2},v_{3})} in ordinary 3D space (our physical space) and apply a rotation matrix R {\displaystyle R} to it. One obtains a rotated vector R v → {\displaystyle

Lagrange, Euler, and Kovalevskaya tops (1,769 words) [view diff] exact match in snippet view article find links to article

{\displaystyle SO(3)} , the three-dimensional rotation group, which is the rotation matrix from the lab frame to the body frame. The full configuration space

Dual lattice (2,028 words) [view diff] exact match in snippet view article find links to article

{\textstyle (qL)^{*}={\frac {1}{q}}L^{*}} . If R {\textstyle R} is a rotation matrix, then ( R L ) ∗ = R L ∗ {\textstyle (RL)^{*}=RL^{*}} . A lattice L

Charts on SO(3) (2,785 words) [view diff] exact match in snippet view article

in an orthogonal 3 × 3 matrix of determinant 1 – in other words, a rotation matrix, but this is a many-to-one map. Note that it is not a covering map

Schwinger function (2,553 words) [view diff] exact match in snippet view article find links to article

\ldots ,x_{n})=S_{n}(Rx_{1}+b,\ldots ,Rx_{n}+b)} for an arbitrary rotation matrix R ∈ S O ( d ) {\displaystyle R\in SO(d)} and an arbitrary translation

Physics beyond the Standard Model (5,521 words) [view diff] exact match in snippet view article find links to article

able to predict lepton masses. The CKM matrix, if interpreted as a rotation matrix in a 3-dimensional vector space, "rotates" a vector composed of square

Triangulation (computer vision) (2,386 words) [view diff] exact match in snippet view article

solution. Let r k {\displaystyle \mathbf {r} _{k}} denote row k of the rotation matrix R {\displaystyle \mathbf {R} } : R = ( − r 1 − − r 2 − − r 3 − ) {\displaystyle

Thomas precession (4,713 words) [view diff] exact match in snippet view article find links to article

perpendicular to the relative velocities; The rotation is given by is a 4×4 rotation matrix R in the axis–angle representation, and coordinate systems are taken

Darboux frame (3,546 words) [view diff] exact match in snippet view article find links to article

be the Euclidean transformation consisting of a translation vi and rotation matrix (Aji). Then the following are readily checked by the invariance of

Kostant's convexity theorem (1,871 words) [view diff] exact match in snippet view article find links to article

Alfred (1954), "Doubly stochastic matrices and the diagonal of a rotation matrix", Amer. J. Math., 76 (3): 620–630, doi:10.2307/2372705, JSTOR 2372705

Hand–eye calibration problem (1,017 words) [view diff] exact match in snippet view article find links to article

this are referred to as separable methods. Where RA represents a 3×3 rotation matrix and tA a 3×1 translation vector, the equation can be broken into two

Hooke's law (9,420 words) [view diff] exact match in snippet view article find links to article

_{rk}l_{sl}c_{ijkl}} where lab are the components of an orthogonal rotation matrix [L]. The same relation also holds for inversions. In matrix notation

Gyrovector space (4,077 words) [view diff] exact match in snippet view article find links to article

\oplus } v). But the resultant boost also needs to be multiplied by a rotation matrix because boost composition (i.e. the multiplication of two 4 × 4 matrices)

Point-set registration (9,086 words) [view diff] exact match in snippet view article find links to article

assumed), R ∈ SO ( 3 ) {\displaystyle R\in {\text{SO}}(3)} is a proper 3D rotation matrix ( SO ( d ) {\displaystyle {\text{SO}}(d)} is the special orthogonal

Icosahedral symmetry (2,349 words) [view diff] exact match in snippet view article find links to article

Rotation matrix Permutation of 5 on 1 2 3 4 5 Permutation of 12 on 1 2 3 4 5 6 7 8 9 10 11 12 M 1 = [ 1 0 0 0 1 0 0 0 1 ] {\displaystyle

Coxeter notation (6,431 words) [view diff] exact match in snippet view article find links to article

3]. The extended group [[3,3,3]], order 240, is doubled by a 2-fold rotation matrix T, here reversing coordinate order and sign: There are 3 generators

Tangent lines to circles (5,203 words) [view diff] exact match in snippet view article find links to article

rotation), and the above equations are rotation of (X, Y) by ±θ using the rotation matrix: ( R ∓ 1 − R 2 ± 1 − R 2 R ) {\displaystyle {\begin{pmatrix}R&\mp {\sqrt

Rigid rotor (6,116 words) [view diff] exact match in snippet view article find links to article

the right hand side indicate time derivatives. Note that a different rotation matrix would result from a different choice of Euler angle convention used

Rigid motion segmentation (3,387 words) [view diff] exact match in snippet view article find links to article

pixel co-ordinate. X'→ transformed pixel co-ordinate. R→ orthonormal rotation matrix with R ⋅ RT = I and |R| = 1. t→ translational vector but in the 2D

Ring laser (5,343 words) [view diff] exact match in snippet view article find links to article

to refer the E-vector after reflection to the new planes with the rotation matrix M r o t = ( cos ⁡ θ sin ⁡ θ − sin ⁡ θ cos ⁡ θ ) {\displaystyle

Canonical transformation (10,413 words) [view diff] exact match in snippet view article find links to article

)=R\mathbf {x} } where R ∈ S O ( 2 ) {\displaystyle R\in SO(2)} is a rotation matrix of order 2 is canonical. Keeping in mind that special orthogonal matrices

Sexological testing (5,300 words) [view diff] exact match in snippet view article find links to article

components was equal to 0.739, 0.765 and 0.751, respectively. The Varimax rotation matrix showed that all questions are applicable to the extracted styles. DAS

Electron backscatter diffraction (13,674 words) [view diff] exact match in snippet view article find links to article

that recalculated the strain after transforming the patterns with a rotation matrix ( R {\displaystyle R} ) calculated from the first cross-correlation