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Dyadic transformation. xy plot where x = x0 ∈ [0, 1] is rational and y = xn for all n. The dyadic transformation (also known as the dyadic map, bit shift map, 2x mod 1 map, Bernoulli map, doubling map or sawtooth map[1][2]) is the mapping (i.e., recurrence relation) (where is the set of sequences from ) produced by the rule. [3]
Other important quotients are the (2, 3, n) triangle groups, which correspond geometrically to descending to a cylinder, quotienting the x coordinate modulo n, as T n = (z ↦ z + n). (2, 3, 5) is the group of icosahedral symmetry, and the (2, 3, 7) triangle group (and associated tiling) is the cover for all Hurwitz surfaces.
Affine group. In mathematics, the affine group or general affine group of any affine space is the group of all invertible affine transformations from the space into itself. In the case of a Euclidean space (where the associated field of scalars is the real numbers), the affine group consists of those functions from the space to itself such that ...
Rijndael MixColumns. The MixColumns operation performed by the Rijndael cipher or Advanced Encryption Standard is, along with the ShiftRows step, its primary source of diffusion. Each column of bytes is treated as a four-term polynomial , each byte representing an element in the Galois field . The coefficients are elements within the prime sub ...
Short-time Fourier transform. Gabor transform. Hankel transform. Hartley transform. Hermite transform. Hilbert transform. Hilbert–Schmidt integral operator. Jacobi transform. Laguerre transform.
The discrete Fourier transform maps an n -tuple of elements of R to another n -tuple of elements of R according to the following formula: {\displaystyle f_ {k}=\sum _ {j=0}^ {n-1}v_ {j}\alpha ^ {jk}.} By convention, the tuple is said to be in the time domain and the index j is called time. The tuple is said to be in the frequency domain and the ...
Polynomial transformations have been applied to the simplification of polynomial equations for solution, where possible, by radicals. Descartes introduced the transformation of a polynomial of degree d which eliminates the term of degree d − 1 by a translation of the roots. Such a polynomial is termed depressed. This already suffices to solve ...
v. t. e. In mathematics, especially in the group theoretic area of algebra, the projective linear group (also known as the projective general linear group or PGL) is the induced action of the general linear group of a vector space V on the associated projective space P (V). Explicitly, the projective linear group is the quotient group.