Search Result for "linear transformation":

The Collaborative International Dictionary of English v.0.48:

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 same breadth throughout, except at the extremities; as, a linear leaf. [1913 Webster] 3. Thinking in a step-by-step analytical and logical fashion; contrasted with holistic, i.e. thinking in terms of complex interrelated patterns; as, linear thinkers. [PJC] Linear thinkers concluded that by taking the world apart, the actions of people were more predictable and controllable. --David Morris (Conference presentation, Fairfield University, October 31, 1997) Linear differential equation (Math.), an equation which is of the first degree, when the expression which is equated to zero is regarded as a function of the dependent variable and its differential coefficients. Linear equation (Math.), an equation of the first degree between two variables; -- so called because every such equation may be considered as representing a right line. Linear measure, the measurement of length. Linear numbers (Math.), such numbers as have relation to length only: such is a number which represents one side of a plane figure. If the plane figure is square, the linear figure is called a root. Linear problem (Geom.), a problem which may be solved geometrically by the use of right lines alone. Linear transformation (Alg.), a change of variables where each variable is replaced by a function of the first degree in the new variable. [1913 Webster]
The Free On-line Dictionary of Computing (30 December 2018):

linear map linear transformation (Or "linear transformation") A function from a vector space to a vector space which respects the additive and multiplicative structures of the two: that is, for any two vectors, u, v, in the source vector space and any scalar, k, in the field over which it is a vector space, a linear map f satisfies f(u+kv) = f(u) + kf(v). (1996-09-30)