The DICT Development Group
2 definitions found
for 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
1. Of or pertaining to a line; consisting of lines; in a
straight direction; lineal.
2. (Bot.) Like a line; narrow; of the same breadth
throughout, except at the extremities; as, a linear leaf.
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.
Linear thinkers concluded that by taking the world
apart, the actions of people were more predictable
and controllable. --David Morris
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.
From The Free On-line Dictionary of Computing (30 December 2018) :
(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).
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