| slovo | definícia |
Linear transformation
(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] |
linear transformation
(foldoc) | 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)
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| | podobné slovo | definícia |
linear transformation
(foldoc) | 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)
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