= Linear function
{wiki}
= Linear
{synonym}
= Linearly
{synonym}
The term is not very clear, as it could either mean:
* a <real number> function whose graph is a line, i.e.:
$$
f(x) = ax + b
$$
or for higher dimensions, a <hyperplane>:
$$
f(x_1, x_2, \ldots, x_n) = c_1 x_1 + c_2 x_2 + \ldots + c_n x_n + b
$$
* a <linear map>. Note that the above linear functions are not linear maps unless $b = 0$ (known as the homogeneous case), because e.g.:
$$
f(x + y) = ax + ay + b
$$
but
$$
f(x) + f(y) = ax + b + ay + b
$$
For this reason, it is better never to refer to linear maps as linear functions.
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