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Toggle the table of contents. Template: Transformation rules. 10 languages. Беларуская (тарашкевіца) ... Print/export Download as PDF;
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 ...
For instance, a "map" is a "continuous function" in topology, a "linear transformation" in linear algebra, etc. Some authors, such as Serge Lang, [8] use "function" only to refer to maps in which the codomain is a set of numbers (i.e. a subset of R or C), and reserve the term mapping for more general functions.
In mathematics, a rotation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x′y′-Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes counterclockwise through an angle .
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication.
Traditionally, data transformation has been a bulk or batch process, [6] whereby developers write code or implement transformation rules in a data integration tool, and then execute that code or those rules on large volumes of data. [7] This process can follow the linear set of steps as described in the data transformation process above.
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In Chomsky's generative grammar framework, the syntax of natural language was described by context-free rules combined with transformation rules. [ 5 ] Block structure was introduced into computer programming languages by the Algol project (1957–1960), which, as a consequence, also featured a context-free grammar [ 6 ] to describe the ...