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; 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]