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  2. Linear map - Wikipedia

    en.wikipedia.org/wiki/Linear_map

    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.

  3. Linear function - Wikipedia

    en.wikipedia.org/wiki/Linear_function

    A constant function is also considered linear in this context, as it is a polynomial of degree zero or is the zero polynomial. Its graph, when there is only one variable, is a horizontal line. In this context, a function that is also a linear map (the other meaning) may be referred to as a homogeneous linear function or a linear form.

  4. Linear function (calculus) - Wikipedia

    en.wikipedia.org/wiki/Linear_function_(calculus)

    In calculus and related areas of mathematics, a linear function from the real numbers to the real numbers is a function whose graph (in Cartesian coordinates) is a non-vertical line in the plane. [1] The characteristic property of linear functions is that when the input variable is changed, the change in the output is proportional to the change ...

  5. Linear fractional transformation - Wikipedia

    en.wikipedia.org/wiki/Linear_fractional...

    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.

  6. Transformation matrix - Wikipedia

    en.wikipedia.org/wiki/Transformation_matrix

    In linear algebra, linear transformations can be represented by matrices.If is a linear transformation mapping to and is a column vector with entries, then there exists an matrix , called the transformation matrix of , [1] such that: = Note that has rows and columns, whereas the transformation is from to .

  7. Transformation (function) - Wikipedia

    en.wikipedia.org/wiki/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, 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.

  8. Conformal linear transformation - Wikipedia

    en.wikipedia.org/.../Conformal_linear_transformation

    Conformal linear transformations come in two types, proper transformations preserve the orientation of the space whereas improper transformations reverse it. As linear transformations, conformal linear transformations are representable by matrices once the vector space has been given a basis , composing with each-other and transforming vectors ...

  9. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

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