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searching for Orthogonal transformation 16 found (42 total)

alternate case: orthogonal transformation

Homogeneous space (1,825 words) [view diff] exact match in snippet view article find links to article

base vector, then any other vector can be constructed using an orthogonal transformation. If we consider the span of this vector as a one dimensional subspace

Euclidean group (2,147 words) [view diff] exact match in snippet view article find links to article

group O(n). Any element of E(n) is a translation followed by an orthogonal transformation (the linear part of the isometry), in a unique way: x ↦ A ( x

Weyl–Brauer matrices (1,647 words) [view diff] exact match in snippet view article find links to article

orthogonal group on the spinors. Consider the application of an orthogonal transformation to the coordinates, which in turn acts upon the Pi via P i ↦ R

Stiefel manifold (2,141 words) [view diff] exact match in snippet view article find links to article

for the action of a classical group in a natural manner. Every orthogonal transformation of a k-frame in R n {\displaystyle \mathbb {R} ^{n}} results in

Integrability conditions for differential systems (1,057 words) [view diff] exact match in snippet view article find links to article

,\phi ^{n})} ⁠, then the two coframes would be related by an orthogonal transformation Φ = M Θ {\displaystyle \Phi =M\Theta } If the connection 1-form

Skew-symmetric matrix (3,632 words) [view diff] exact match in snippet view article find links to article

every skew-symmetric matrix to a block diagonal form by a special orthogonal transformation. Specifically, every 2 n × 2 n {\displaystyle 2n\times 2n} real

Zonal spherical harmonics (866 words) [view diff] exact match in snippet view article find links to article

)}(R\mathbf {y} )=Z_{\mathbf {x} }^{(\ell )}(\mathbf {y} )} for every orthogonal transformation R. Conversely, any function f(x,y) on Sn−1×Sn−1 that is a spherical

Pin group (2,502 words) [view diff] exact match in snippet view article find links to article

v_{k})^{-1}} , which is the composition of k reflections. Since every orthogonal transformation can be expressed as a composition of reflections (the Cartan–Dieudonné

Covariance matrix (5,799 words) [view diff] exact match in snippet view article find links to article

{\Sigma _{X}} } is symmetric, it can be diagonalized by a linear orthogonal transformation, i.e. there exists such orthogonal matrix A {\displaystyle \mathbf

Spinors in three dimensions (2,626 words) [view diff] exact match in snippet view article find links to article

of two reflections. (More generally, any orientation-reversing orthogonal transformation is either a reflection or the product of three reflections.) Thus

Inner product space (7,357 words) [view diff] exact match in snippet view article find links to article

weighted-sum version of the dot product with positive weights—up to an orthogonal transformation. The article on Hilbert spaces has several examples of inner product

Levi-Civita symbol (5,174 words) [view diff] exact match in snippet view article find links to article

However, the Levi-Civita symbol is a pseudotensor because under an orthogonal transformation of Jacobian determinant −1, for example, a reflection in an odd

Common integrals in quantum field theory (6,052 words) [view diff] exact match in snippet view article find links to article

matrix. This integral is performed by diagonalization of A with an orthogonal transformation D = O − 1 A O = O T A O {\displaystyle D=O^{-1}AO=O^{\text{T}}AO}

History of Lorentz transformations (15,399 words) [view diff] exact match in snippet view article find links to article

Wikiversity: History of Lorentz transformations via imaginary orthogonal transformation includes contributions of Sophus Lie (1871), Hermann Minkowski

600-cell (28,920 words) [view diff] exact match in snippet view article find links to article

screw-displacement, and Q2 is a double rotation (in four dimensions). Every orthogonal transformation is expressible as Qq Rr where 2q + r ≤ n, the number

24-cell (30,655 words) [view diff] exact match in snippet view article find links to article

screw-displacement, and Q2 is a double rotation (in four dimensions). Every orthogonal transformation is expressible as Qq Rr where 2q + r ≤ n, the number