the.com/linear transformation

means A function between vector spaces that preserves addition and scalar multiplication — meaning it respects straight lines through the origin and evenly spaced grids, never warping them into curves.

from 'Linear' traces back to Latin linea, 'a line made by a pencil or thread' — itself from linum, 'flax,' the stuff linen thread was spun from. 'Transformation' comes from Latin trans- ('across') plus formare ('to shape'), so literally 'a reshaping across.' The mathematical sense of 'linear' narrowed over the 1700s–1800s from merely 'line-related' to the stricter idea of functions satisfying f(x+y)=f(x)+f(y) and f(cx)=cf(x) — a meaning stretched, like the transformations themselves, far beyond its humble thread-and-pencil origins.