linear function


Also found in: Wikipedia.

linear function

[′lin·ē·ər ′fəŋk·shən]
(mathematics)

Linear Function

 

a function of the form y = kx + b. The basic property of a linear function is that an increment in the function is proportional to the corresponding increment in the independent variable. The graph of a linear function is a straight line. If we use the same units on the coordinate axes, then the coefficient k (the slope) is equal to the tangent of the angle formed by the line with the Ox axis (k = tan ϕ; see Figure 1) and b is the segment cut off by the line on the Oy axis. When b = 0, the linear function is called homogeneous; its graph depicts the direct proportion: y = kx.

Figure 1

Linear functions are widely used in physics and engineering in order to represent (often approximately) the dependence of various quantities. Linear functions of several variables are also studied. Homogeneous linear functions of several variables are called linear forms. Homogeneous linear functions which send vectors to vectors are called linear transformations.

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.
References in periodicals archive ?
The trends of the phenomena are described by a linear function and a 6th degree polynomial.
5, which is a linear function of k and thus cannot describe the behaviour depicted by figure 4 in Warren (2004).
1) is approximately a linear function of the applied force F, the standard uncertainty, [u.
There are two basic forms of the dose-response function for lead: a simple linear model, in which the increase in health effect is a linear function of increasing blood lead concentration (BPb), and a nonlinear model, in which the amount of health effect change attributable to lead changes according the region of the dose-response curve studied.
However, the availability of suitable mosquito habitats is not a simple linear function of rainfall.
Since all subpopulations were derived from cycle 0, the definitions of the above terms are: A0 = contribution of additive effects from Golden Glow at C0; D0 = contribution of dominance effects from Golden Glow at C0; ALI = linear function of changes in allelic frequencies influencing additive effects in subpopulation I; DLI = linear function of changes in allelic frequencies influencing dominance effects in subpopulation I; DQ I = quadratic function of changes in .
Based on the equation given in the introduction for a sinusoidal strain cycle, we anticipate that the hysteresis should be a linear function of the shear strain squared, if compression did not affect the material behavior.
This study also suggests using inductive multimedia programs that include the coordinate graph teaching strategy for the problem of translation, specifically creation of linear function.
6 shows the image after correction using the linear function generated together with the nearest neighbour resampling technique.
Equation 1 expresses the equilibrium unemployment rate as a negative linear function of the current inflation rate and a positive linear function of the inflation rate lagged one year; this would be identical to the NAIRU relation if the coefficients b and c are equal.
The interpretation of m as the scale of the x-axis was unexpected, particularly because the nature of a linear function is not dependent upon the value chosen for the scale of either axis.