Vector (Applied Mathematics)

In applied mathematics, a vector is a list of scalars of fixed length. They can be denoted by raising a base ($\mathbb{R}$ or $\mathbb{C}$) to an integer power. For example,

$$\vec{x}:{\mathbb{R}}^5=\left(\begin{array}{c}1.1\\ 2.2\\ 3.3\\ 4.4\\ 5.5\end{array}\right)$$

Vectors are written either in bold or with an arrow on top, to distinguish them from scalars.

Vectors are indexed with integer sub-scripts starting at 1:

$${\vec{x}}_4=4.4$$

This notion is related to but should be distinguished from vector spaces. These are a theoretical notion. In general, all applied math vector types are also vector spaces in the theoretical sense. But there are vector spaces that can’t be represented by raising a scalar to an integer power.