Definition:Column Matrix

From ProofWiki
Jump to navigation Jump to search

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 a column matrix is an element of a vector space, it is often referred to as a column vector.


Also see

  • Results about column matrices can be found here.


Sources

Retrieved from "https://proofwiki.org/w/index.php?title=Definition:Column_Matrix&oldid=658187"