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Linear fractional transformations leave cross ratio invariant, so any linear fractional transformation that leaves the unit disk or upper half-planes stable is an isometry of the hyperbolic plane metric space. Since Henri Poincaré explicated these models they have been named after him: the Poincaré disk model and the Poincaré half-plane model.
In mathematics, a transformation, transform, or self-map [1] is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f: X → X. [ 2 ] [ 3 ] [ 4 ] Examples include linear transformations of vector spaces and geometric transformations , which include projective transformations , affine transformations , and ...
More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polytope , which is a set defined as the intersection of finitely many half spaces , each of which is defined by a linear inequality.
For example, every integral transform is a linear operator, since the integral is a linear operator, and in fact if the kernel is allowed to be a generalized function then all linear operators are integral transforms (a properly formulated version of this statement is the Schwartz kernel theorem).
In electrical engineering, the alpha-beta transformation (also known as the Clarke transformation) is a mathematical transformation employed to simplify the analysis of three-phase circuits. Conceptually it is similar to the dq0 transformation .
Abebe Bikila was born on August 7, 1932, in the small community of Jato, then part of the Selale District of Shewa. [8] His birthday coincided with the 1932 Los Angeles Olympic marathon . [ 9 ] Abebe was the son of Wudinesh Beneberu and her second husband, Demissie. [ 10 ]