the.com/vector space

means A collection of objects (vectors) that can be added together and scaled by numbers, while still following a fixed set of consistent rules — the basic setting for most of linear algebra.

from "Vector" comes from Latin vehere, "to carry" (the same root as vehicle), first used in the 1700s for quantities with magnitude and direction, like a displacement that carries a point from one place to another. "Space" as a mathematical container dates to 19th-century geometry, when mathematicians like Hermann Grassmann and later Giuseppe Peano began treating collections of objects abstractly as places where operations like addition and scaling could live, detached from any physical picture. The formal axioms we use today were essentially fixed by Peano in 1888, giving "vector space" its modern sense: not a place you walk through, but a structure you calculate in.