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Was (wer) ist linear function - definition
AMBIGUOUS MATHEMATICAL TERM
Linear functions; Linear factor; Linear factors; Linear growth; Arithmetic growth
![The [[integral]] of a function is a linear map from the vector space of integrable functions to the real numbers.](https://commons.wikimedia.org/wiki/Special:FilePath/Integral as region under curve.svg?width=200 "The [[integral]] of a function is a linear map from the vector space of integrable functions to the real numbers.")
linear function
A recursive function is linear if it is of the form
f x = if p x then q x else h f x
where h is a "linear functional" which means that
(1) for all functions, a, b c and some function ht
h (if a then b else c) = if ht a then h b else h c
Function ht is known as the "predicate transformer" of h.
(2) If for some x,
h ( y . bottom) x /= bottom
then
for all g, ht g x = True.
I.e. if h g x terminates despite g x not terminating then ht g
x doesn't depend on g.
See also linear argument.
(1995-02-15)
Linear function
In mathematics, the term linear function refers to two distinct but related notions:"The term linear function means a linear form in some textbooks and an affine function in others." Vaserstein 2006, p.
linear map
MAPPING THAT PRESERVES THE OPERATIONS OF ADDITION AND SCALAR MULTIPLICATION
Linear operator; Linear mapping; Linear transformations; Linear operators; Linear transform; Linear maps; Linear isomorphism; Linear isomorphic; Linear Transformation; Linear Transformations; Linear Operator; Homogeneous linear transformation; User:The Uber Ninja/X3; Linear transformation; Bijective linear map; Nonlinear operator; Linear Schrödinger Operator; Vector space homomorphism; Vector space isomorphism; Linear extension of a function; Linear extension (linear algebra); Extend by linearity; Linear endomorphism
<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)
Wikipedia
Linear function
In mathematics, the term linear function refers to two distinct but related notions:
- In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one. For distinguishing such a linear function from the other concept, the term affine function is often used.
- In linear algebra, mathematical analysis, and functional analysis, a linear function is a linear map.
