# Definition:Column Matrix

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## Definition

A **column matrix** is an $m \times 1$ matrix:

- $\mathbf C = \begin {bmatrix} c_{1 1} \\ c_{2 1} \\ \vdots \\ c_{m 1} \end {bmatrix}$

That is, it is a matrix with only one column.

## Row Presentation

When presenting a **column matrix** on the printed page, the decision is often made to save space by presenting it horizontally instead of vertically.

However, it is not then straightforward to recognise that a **column matrix**, and not a **row matrix**, is meant.

Hence, in order to alleviate the confusion, braces are often used as delimiters for such a presentation.

Thus the **column matrix** $\mathbf C$ above would then be presented as:

- $\mathbf C = \set {\begin {matrix} c_{1 1} &c_{2 1} & \cdots & c_{m 1} \end {matrix} }$

## Also known as

If such a matrix is an element of a vector space, it is also called a **column vector**.

## Also see

## Sources

- 1954: A.C. Aitken:
*Determinants and Matrices*(8th ed.) ... (previous) ... (next): Chapter $\text I$: Definitions and Fundamental Operations of Matrices: $4$. Matrices, Row Vectors, Column Vectors, Scalars - 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 30$. Linear Equations - 1980: A.J.M. Spencer:
*Continuum Mechanics*... (previous) ... (next): $2.1$: Matrices