**Definition:** A *vector* is an ordered list of \(n\) scalars from a field \(\mathbb{F}\).
A vector in \(\mathbb{F}^n\) can be written as:
\[\mathbf{v} = (v_1, v_2, \ldots, v_n)\]
where each \(v_j \in \mathbb{F}\) is called a *component* (or *entry*) of the vector.
**Notation:** Vectors are typically denoted by boldface lowercase letters: \(\mathbf{u}\), \(\mathbf{v}\), \(\mathbf{w}\), etc.
**Two common representations:**
- **Row vector:** \(\mathbf{v} = (v_1, v_2, \ldots, v_n)\) — written horizontally
- **Column vector:** \(\mathbf{v} = \begin{pmatrix} v_1 \\ v_2 \\ \vdots \\ v_n \end{pmatrix}\) — written vertically
**Examples:**
- \(\mathbf{v} = (3, -1, 0) \in \mathbb{R}^3\)
- \(\mathbf{w} = (1+i, 2-i) \in \mathbb{C}^2\)