Note 1 to entry: 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 to entry: A vector in a Euclidean space is characterized by its magnitude and, if it is a non-zero vector, by its direction.

Note 3 to entry: 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 to entry: 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 to entry: The term "vector" is also used for a vector quantity.

Note 6 to entry: In geometry, the term “vector” is often used for a directed line segment in a point space.