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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.
Transformation (function) A composition of four mappings coded in SVG, which transforms a rectangular repetitive pattern. into a rhombic pattern. The four transformations are linear. In mathematics, a transformation 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 ...
In mathematics, transformation geometry (or transformational geometry) is the name of a mathematical and pedagogic take on the study of geometry by focusing on groups of geometric transformations, and properties that are invariant under them. It is opposed to the classical synthetic geometry approach of Euclidean geometry, that focuses on ...
In linear algebra and functional analysis, a projection is a linear transformation from a vector space to itself (an endomorphism) such that . That is, whenever is applied twice to any vector, it gives the same result as if it were applied once (i.e. is idempotent). It leaves its image unchanged. [1]
Short-time Fourier transform. Gabor transform. Hankel transform. Hartley transform. Hermite transform. Hilbert transform. Hilbert–Schmidt integral operator. Jacobi transform. Laguerre transform.
The blue line is the common solution to two of these equations. Linear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. [1][2][3] Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental ...
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