# Definition of size of a vector

Put content here**Definition:** The *size* (or *dimension*) of a vector \(\mathbf{v} \in \mathbb{F}^n\) is the number \(n\) of its components.
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If \(\mathbf{v} = (v_1, v_2, \ldots, v_n)\), then the size of \(\mathbf{v}\) is \(n\).
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**Notation:** The size of \(\mathbf{v}\) is often denoted as:
- \(\text{size}(\mathbf{v}) = n\)
- \(\mathbf{v} \in \mathbb{F}^n\) (the superscript indicates the size)
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**Examples:**
- \(\mathbf{v} = (3, -1, 0, 5)\) has size 4, so \(\mathbf{v} \in \mathbb{R}^4\)
- \(\mathbf{w} = (1+i, 2-i)\) has size 2, so \(\mathbf{w} \in \mathbb{C}^2\)
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**Important:** Two vectors can only be added if they have the same size. Vector operations are defined component-wise, so mismatched sizes make the operation undefined.

# Parents

* Algebraic properties of R^n (or C^n)