# Definition of column vector

Put content here**Definition:** A *column vector* is a vector written as a vertical array of \(n\) entries:
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\[\mathbf{v} = \begin{pmatrix} v_1 \\ v_2 \\ \vdots \\ v_n \end{pmatrix}\]
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where each \(v_j \in \mathbb{F}\).
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**Notation:** Column vectors are often denoted using parentheses or square brackets:
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\[\mathbf{v} = \begin{bmatrix} v_1 \\ v_2 \\ \vdots \\ v_n \end{bmatrix}\]
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**Why column vectors?** Column vectors are the standard representation in linear algebra because:
- They align naturally with matrix-vector multiplication \(A\mathbf{x}\)
- They correspond to elements of \(\mathbb{F}^n\) as column spaces
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**Example:**
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\[\mathbf{v} = \begin{pmatrix} 3 \\ -1 \\ 0 \end{pmatrix} \in \mathbb{R}^3\]
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The **transpose** of a column vector is a row vector: \(\mathbf{v}^T = (3, -1, 0)\).

# Parents

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