Linear transformation

from 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]
    
from The Free On-line Dictionary of Computing (8 July 2008)
linear map
linear transformation

   <mathematics> (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)
    

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