Vector

A vector is an element of a vector space. In $\mathbb{R}^n$, a vector is an ordered $n$-tuple of real numbers such as $(3, -1, 4)$. But vectors need not be tuples of numbers — polynomials, functions, and many other objects can be vectors, provided their containing set satisfies the vector space axioms.

A vector is characterized not by what it “is” but by what operations it supports: it can be added to other vectors and scaled by elements of the underlying field.