A vector is formally defined within linear algebra as a mathematical object that possesses properties allowing for sensible addition and scalar multiplication operations, subsuming distinct perspectives such as physical arrows in Euclidean space and ordered lists of numbers (lists). In two-dimensional domains like the XY plane, vectors are represented by pairs of coordinates relative to an origin, while three-dimensional representations utilize triplets via the perpendicular Z-axis. This abstract concept serves as a fundamental building block that enables the translation between geometric intuition regarding spatial manipulation and computational algorithms involving data structures or matrix operations in broader mathematical disciplines.
A vector is formally defined within linear algebra as a mathematical object that possesses properties allowing for sensible addition and scalar multiplication operations, subsuming distinct perspecti…