linear transformation

a map from one vector space to a vector space having the same field of scalars, with the properties that the map of the sum of two vectors is the sum of the maps of the vectors and the map of a scalar times a vector equals the scalar times the map of the vector. Also called linear function.
[1885-90]

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In mathematics, a rule for changing one geometric figure (or matrix or vector) into another using a formula with a specified format.

The format must be a linear combination, in which the original components (e.g., the x and y coordinates of each point of the original figure) are changed via the formula ax + by to produce the coordinates of the transformed figure. Examples include flipping the figure over the x or y axis, stretching or compressing it, and rotating it. Every such transformation has an inverse, which undoes its effect.

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Universalium. 2010.

Look at other dictionaries:

  • Linear transformation — Linear Lin e*ar (l[i^]n [ e]*[ e]r), a. [L. linearis, linearius, fr. linea line: cf. F. lin[ e]aire. See 3d {Line}.] 1. Of or pertaining to a line; consisting of lines; in a straight direction; lineal. [1913 Webster] 2. (Bot.) Like a line;… …   The Collaborative International Dictionary of English

  • linear transformation — tiesinė transformacija statusas T sritis fizika atitikmenys: angl. linear transformation vok. lineare Transformation, f rus. линейное преобразование, n pranc. transformation linéaire, f …   Fizikos terminų žodynas

  • linear transformation — tiesinė transformacija statusas T sritis automatika atitikmenys: angl. linear transformation vok. Lineartransformation, f rus. линейное преобразование, n pranc. transformation linéaire, f …   Automatikos terminų žodynas

  • linear transformation — linear change, one dimensional change …   English contemporary dictionary

  • linear transformation — noun 1. : a transformation in which the new variables are linear functions of the old variables 2. : a function that maps the vectors of one vector space onto the vectors of the same or another vector space with the same field of scalars in such… …   Useful english dictionary

  • linear transformation — noun Date: circa 1846 1. a transformation in which the new variables are linear functions of the old variables 2. a function that maps the vectors of one vector space onto the vectors of the same or another vector space with the same field of… …   New Collegiate Dictionary

  • linear transformation — noun A map between vector spaces which respects addition and multiplication. Syn: linear map …   Wiktionary

  • Direct linear transformation — (DLT) is an algorithm which solves a set of variables from a set of similarity relations:   for where and are known vectors, denotes equality up to an unknown scalar multiplication, and …   Wikipedia

  • Linear — Lin e*ar (l[i^]n [ e]*[ e]r), a. [L. linearis, linearius, fr. linea line: cf. F. lin[ e]aire. See 3d {Line}.] 1. Of or pertaining to a line; consisting of lines; in a straight direction; lineal. [1913 Webster] 2. (Bot.) Like a line; narrow; of… …   The Collaborative International Dictionary of English

  • Linear differential equation — Linear Lin e*ar (l[i^]n [ e]*[ e]r), a. [L. linearis, linearius, fr. linea line: cf. F. lin[ e]aire. See 3d {Line}.] 1. Of or pertaining to a line; consisting of lines; in a straight direction; lineal. [1913 Webster] 2. (Bot.) Like a line;… …   The Collaborative International Dictionary of English

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