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  2. Homothety - Wikipedia

    en.wikipedia.org/wiki/Homothety

    Here is the ratio of magnification or dilation factor or scale factor or similitude ratio. Such a transformation can be called an enlargement if the scale factor exceeds 1. The above-mentioned fixed point S is called homothetic center or center of similarity or center of similitude.

  3. Scaling (geometry) - Wikipedia

    en.wikipedia.org/wiki/Scaling_(geometry)

    Each iteration of the Sierpinski triangle contains triangles related to the next iteration by a scale factor of 1/2. In affine geometry, uniform scaling (or isotropic scaling [1]) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions (isotropically).

  4. Scale invariance - Wikipedia

    en.wikipedia.org/wiki/Scale_invariance

    In physics, mathematics and statistics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor, and thus represent a universality. The technical term for this transformation is a dilatation (also known as dilation).

  5. Conformal linear transformation - Wikipedia

    en.wikipedia.org/wiki/Conformal_linear...

    Because every reflection across a hyperplane reverses the orientation of a pseudo-Euclidean space, the composition of any even number of reflections and a dilation by a positive real number is a proper conformal linear transformation, and the composition of any odd number of reflections and a dilation is an improper conformal linear transformation.

  6. Scaling dimension - Wikipedia

    en.wikipedia.org/wiki/Scaling_dimension

    In a scale invariant quantum field theory, by definition each operator acquires under a dilation a factor , where is a number called the scaling dimension of . This implies in particular that the two point correlation function O ( x ) O ( 0 ) {\displaystyle \langle O(x)O(0)\rangle } depends on the distance as ( x 2 ) − Δ {\displaystyle (x^{2 ...

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  8. Dilation - Wikipedia

    en.wikipedia.org/wiki/Dilation

    Dilation (operator theory), a dilation of an operator on a Hilbert space; Dilation (morphology), an operation in mathematical morphology; Scaling (geometry), including: Homogeneous dilation , the scalar multiplication operator on a vector space or affine space; Inhomogeneous dilation, where scale factors may differ in different directions

  9. Dilation (morphology) - Wikipedia

    en.wikipedia.org/wiki/Dilation_(morphology)

    Dilation is commutative, also given by = =. If B has a center on the origin, then the dilation of A by B can be understood as the locus of the points covered by B when the center of B moves inside A. The dilation of a square of size 10, centered at the origin, by a disk of radius 2, also centered at the origin, is a square of side 14, with ...

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