Quadratic Transformation (other)
In mathematics, a quadratic transformation may be *A quadratic transformation in the Cremona group In birational geometry, the Cremona group, named after Luigi Cremona, is Birational geometry#Birational automorphism groups, the group of birational automorphisms of the n-dimensional projective space over a Field (mathematics), field , also known a ... * Kummer's quadratic transformation of the hypergeometric function {{mathdab ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  

Cremona Group
In birational geometry, the Cremona group, named after Luigi Cremona, is Birational geometry#Birational automorphism groups, the group of birational automorphisms of the n-dimensional projective space over a Field (mathematics), field , also known as Cremona transformations. It is denoted by Cr(\mathbb^n(k)), Bir(\mathbb^n(k)) or Cr_n(k). Historical origins The Cremona group was introduced by the italian mathematician . However, some historians consider Isaac Newton as a "founder of the theory of Cremona transformations" through his work done two centuries before, in 1667 and 1687. Contributions were also made by Hilda Phoebe Hudson in the 1900s. Basic properties The Cremona group is naturally identified with the automorphism group \mathrm_k(k(x_1, ..., x_n)) of the rational function, field of the rational functions in n Indeterminate (variable), indeterminates over k. Here, the field k(x_1, ..., x_n) is a pure transcendental extension of k, with transcendence degree n. The p ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]