1. element of a vector space
2. directed line segment in a point space

NOTE 1 An n-dimensional vector is represented by an ordered set of n scalars, usually real or complex numbers, which depend on the choice of the base. In matrix notation, these scalars are usually represented as a column matrix:
$U=\left(\begin{array}{c}{U}_1\\ U_2\\ ⋮\\ U_n\end{array}\right)$

NOTE 2 A vector in a Euclidean space is characterized by its magnitude (102-03-23) and, if it is a non-zero vector, by its direction (102-03-12).

NOTE 3 A complex vector U is defined by a real part and an imaginary part:
$U=A+jB$ where A and B are real vectors.

NOTE 4 A vector is indicated by a letter symbol in sloped boldface type or by an arrow above a sloped lightface letter symbol: U or $\overrightarrow{U}$. The vector U with components $U_i$ can be denoted $(U_i)$.

NOTE 5 The term "vector" is also used for a vector quantity (102-03-21).