In linear algebra, a squeeze mapping, also called a squeeze transformation, is a type of linear map that preserves Euclidean area of regions in the Cartesian...
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Affine transformation (redirect from Affine mapping)
with a homothety and a translation, shear mapping combined with a homothety and a translation, or squeeze mapping combined with a homothety and a translation...
27 KB (3,594 words) - 00:41, 22 August 2024
{\displaystyle e^{bj}\!} then corresponds under this linear transformation to a squeeze mapping σ : ( u , v ) ↦ ( r u , v r ) , r = e b . {\displaystyle \sigma :(u...
27 KB (4,057 words) - 01:57, 2 May 2024
has been used to define hyperbolic distance in a geometry textbook. Squeeze mapping V.G. Ashkinuse & Isaak Yaglom (1962) Ideas and Methods of Affine and...
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m=1/n} or n = 1 / m {\displaystyle n=1/m} , the transformation is a squeeze mapping. Mathematics portal 2D_computer_graphics#Scaling Digital zoom Dilation...
10 KB (1,610 words) - 14:19, 9 May 2024
hyperbola the turning is by squeeze mapping, and the hyperbolic angle magnitudes stay the same when the plane is squeezed by a mapping (x, y) ↦ (rx, y / r),...
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{\ell }{k}}b,\ b)} shear mapping ∼ ( k a + ℓ b , 1 k b ) {\displaystyle \thicksim (ka+\ell b,\ {\tfrac {1}{k}}b)} squeeze mapping ∼ ( k a + ℓ b , 1 k...
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change), so objects effectively undergo a squeeze mapping, properly an inhomogeneous squeeze (magnitude of squeeze varies with distance to the camera), hence...
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hyperbolic angle is invariant under squeeze mapping, and a difference of slopes is invariant under shear mapping. Ergodic theory is the study of invariant...
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dynamical systems Bifurcation, of an incompressible flow, modeled by squeeze mapping the fluid flow River bifurcation, the forking of a river into its tributaries...
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algebra, precursor to Minkowski space Hyperbolic rotation, a synonym for squeeze mapping Hyperbolic sector, a planar region demarcated by radial lines and a...
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dimension Examples of vector spaces Linear map Shear mapping or Galilean transformation Squeeze mapping or Lorentz transformation Linear subspace Row and...
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Charts on SO(3) Rotations and reflections in two dimensions CORDIC Squeeze mapping Infinitesimal rotation matrix Irrational rotation Orientation (geometry)...
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a rectangle may be obtained by applying a squeeze mapping to the square. Another way to view these mappings is via hyperbolic sectors. Starting from (1...
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Equiareal map (redirect from Equiareal mapping)
converse is not true. In fact, shear mapping and squeeze mapping are counterexamples to the converse. Shear mapping takes a rectangle to a parallelogram...
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Transformation matrix (section Squeezing)
with reciprocal values, then the transformation matrix represents a squeeze mapping: [ k 0 0 1 / k ] . {\displaystyle {\begin{bmatrix}k&0\\0&1/k\end{bmatrix}}...
24 KB (3,814 words) - 14:27, 28 July 2024
and is a shear mapping. If | t r ( A ) | > 2 {\displaystyle |\mathrm {tr} (A)|>2} , then A is called hyperbolic, and is a squeeze mapping. The names correspond...
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Axial ratio Ratio Equidimensional ratios in 3D List of film formats Squeeze mapping Scale (ratio) Vertical orientation Rouse, Margaret (September 2005)...
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A real m-by-n matrix A gives rise to a linear transformation Rn → Rm mapping each vector x in Rn to the (matrix) product Ax, which is a vector in Rm...
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The hyperbolic angle is an invariant measure with respect to the squeeze mapping, just as the circular angle is invariant under rotation. The Gudermannian...
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plane isometries are mappings that preserve area, but the converse is false as shown by counterexamples shear mapping and squeeze mapping. Other examples include...
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invariant under rotation, and hyperbolic angle measure is invariant under squeeze mapping. The Haar measure for a locally compact topological group is a generalization...
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transformation that takes a square to a rectangle of the same area (a squeeze mapping) has reciprocal eigenvalues. The eigendecomposition of a symmetric...
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Linear map (redirect from Linear mapping)
{A} ={\begin{pmatrix}1&-\sin \theta \\0&\cos \theta \end{pmatrix}}} squeeze mapping: A = ( k 0 0 1 k ) {\displaystyle \mathbf {A} ={\begin{pmatrix}k&0\\0&{\frac...
43 KB (7,001 words) - 21:10, 13 July 2024
involves rapidity instead of velocity, and substitutes squeeze mapping for the shear mapping used earlier. This affine geometry was developed synthetically...
20 KB (2,632 words) - 15:31, 19 June 2024
stay constant as the density-temperature quadrant (ρ,T) undergoes a squeeze mapping. The adjective "isobaric" is derived from the Greek words ἴσος (isos)...
12 KB (1,891 words) - 11:28, 12 May 2024
In calculus, the squeeze theorem (also known as the sandwich theorem, among other names) is a theorem regarding the limit of a function that is bounded...
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(invariant under rotation) and hyperbolic angle, with invariance group of squeeze mappings. The concept of a slope or gradient is also used as a basis for developing...
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p) is known as the split orthogonal group. The basic example is the squeeze mappings, which is the group SO+(1, 1) of (the identity component of) linear...
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boost in the ( t , x ) {\displaystyle (t,x)} plane shows up as the squeeze mapping x + → e + β x + {\displaystyle x^{+}\to e^{+\beta }x^{+}} , x − → e...
7 KB (1,362 words) - 04:31, 28 January 2024