Noun
(mathematics) Any function whose graph is a straight line:
f
(
x
)
=
a
x
+
b
{\displaystyle f(x)=ax+b}
(mathematics) Any function whose value on the sum of two elements is the sum of the values of the function on the two elements and whose value on the product of a scalar times an element is the scalar times the value of the function on the element:
f
(
a
x
+
b
y
)
=
a
f
(
x
)
+
b
f
(
y
)
{\displaystyle f(ax+by)=af(x)+bf(y)}
Algebra and geometry *If y is a linear function of x, then the coefficient of x is the slope of the line created by plotting the function. Source: Internet
A function which satisfies these properties is called a linear function (or linear operator, or more generally a linear map ). Source: Internet
A partial differential equation (PDE) for the function is an equation of the form : If f is a linear function of u and its derivatives, then the PDE is called linear. Source: Internet
In other words, we would like the sum of all right hand side of the constraints to be the maximal under the condition that for each primal variable the sum of its coefficients do not exceed its coefficient in the linear function. Source: Internet
Non-linearity All ADCs suffer from non-linearity errors caused by their physical imperfections, causing their output to deviate from a linear function (or some other function, in the case of a deliberately non-linear ADC) of their input. Source: Internet
Sometimes the term linear function has the same meaning as linear map, while in analytic geometry it does not. Source: Internet