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What (who) is linear function - definition

AMBIGUOUS MATHEMATICAL TERM

Linear functions; Linear factor; Linear factors; Linear growth; Arithmetic growth

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.

https://en.wikipedia.org/wiki/Linear_function

linear map

$The function f:\R^2 \to \R^2 with f(x, y) = (2x, y) is a linear map. This function scales the x component of a vector by the factor 2.$
$The function f(x, y) = (2x, y) is additive: It doesn't matter whether vectors are first added and then mapped or whether they are mapped and finally added: f(\mathbf a + \mathbf b) = f(\mathbf a) + f(\mathbf b)$
$The function f(x, y) = (2x, y) is homogeneous: It doesn't matter whether a vector is first scaled and then mapped or first mapped and then scaled: f(\lambda \mathbf a) = \lambda f(\mathbf a)$

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.

https://en.wikipedia.org/wiki/Linear function