'Linear transformation' definitions:

Definition of 'Linear transformation'

From: GCIDE
  • 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]