On Physics Stack Exchange, the question was asked: Are lorentz transformations linear?
The up-votes given to an answer seemed to be in proportion to how mathematically sophisticated it was, with mine right at the bottom with zero votes; stating that a plot of the transformed variable against the independent untransformed variables is a straight line. After all, linear comes from Latin linearis "belonging to a line,"
Is a linear transformation just a mathematical description of a straight line?
Excuse me for my bad formalism, I'm no mathematician. Linear is a transformation $T$ from a vector space $X$ to $Y$ when $T(x_1+x_2)=T(x_1)+T(x_2)$ and $T(ax)=a\ T(x)$ if $a$ is a constant, and $x_1$, $x_2$, $x$ are vectors in a vector space $X$. Once again: this is NOT a correct formalization, but purely to grasp the concept of what "linear" in this case means.
Anyway, when I first heard about it, I also thought it has to do something with lines.