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quadratic transformation

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  • Quadratic form — In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. For example, is a quadratic form in the variables x and y. Quadratic forms occupy a central place in various branches of mathematics, including… …   Wikipedia

  • Möbius transformation — Not to be confused with Möbius transform or Möbius function. In geometry, a Möbius transformation of the plane is a rational function of the form of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − …   Wikipedia

  • Complex quadratic polynomial — A complex quadratic polynomial is a quadratic polynomial whose coefficients are complex numbers. Contents 1 Forms 2 Conjugation 2.1 Between forms 2.2 With doubling map …   Wikipedia

  • Legendre transformation — f(x) . The function is shown in red, and the tangent line at point (x 0, f(x 0)) is shown in blue. The tangent line intersects the vertical axis at (0, f^star) and f^star is the value of the Legendre transform f^star(p 0) , where p 0=dot{f}(x 0) …   Wikipedia

  • 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… …   Wikipedia

  • Möbius transformation/Proofs — Fixed PointsThe article claims that for c e 0, the two roots are :gamma = frac{(a d) pm sqrt{(a d)^2 + 4 c b{2 c}of the quadratic equation:c gamma^2 (a d) gamma b = 0 ,which follows from the fixed point equation : gamma=agamma +b}over {cgamma +d… …   Wikipedia

  • Linear canonical transformation — Paraxial optical systems implemented entirely with thin lenses and propagation through free space and/or graded index (GRIN) media, are Quadratic Phase Systems (QPS). The effect of any arbitrary QPS on an input wavefield can be described using… …   Wikipedia

  • Blowing up — This article is about the mathematical concept of blowing up. For information about the physical/chemical process, see Explosion. For other uses of Blow up , see Blow up (disambiguation). Blowup of the affine plane. In mathematics, blowing up or… …   Wikipedia

  • Buddhabrot — A Buddhabrot iterated to 20,000 times. The Buddhabrot is a map related to the Mandelbrot set. Its name reflects its similarity to classical depictions of Gautama Buddha, seated in a meditation pose with a forehead mark (tikka) and traditional… …   Wikipedia

  • Cyclostationary process — A cyclostationary process is a signal having statistical properties that vary cyclically with time.[1] A cyclostationary process can be viewed as multiple interleaved stationary processes. For example, the maximum daily temperature in New York… …   Wikipedia

  • Cremona group — In mathematics, in birational geometry, the Cremona group (named for Luigi Cremona) of order n over a field k is the group of birational automorphisms of the n dimensional projective space over k. It is denoted by Cr(Pn(k)) or Bir(Pn(k)) or… …   Wikipedia

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