Editing Row and column vectors (section)

== Notation ==

To simplify writing column vectors in-line with other text, sometimes they are written as row vectors with the transpose operation applied to them.

<math display="block">\boldsymbol{x} = \begin{bmatrix} x_1 \; x_2 \; \dots \; x_m \end{bmatrix}^{\rm T}</math>

or

<math display="block">\boldsymbol{x} = \begin{bmatrix} x_1, x_2, \dots, x_m \end{bmatrix}^{\rm T}</math>

Some authors also use the convention of writing both column vectors and row vectors as rows, but separating row vector elements with [[comma]]s and column vector elements with [[semicolon]]s (see alternative notation 2 in the table below).{{fact|date=March 2021}}
{| class="wikitable"
|-
! !! Row vector !! Column vector
|-
| '''Standard matrix notation'''<br/>(array spaces, no commas, transpose signs)
| align=center| <math> \begin{bmatrix} x_1 \; x_2 \; \dots \; x_m \end{bmatrix} </math> 
| align=center| <math> \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_m \end{bmatrix} \text{ or } \begin{bmatrix} x_1 \; x_2 \; \dots \; x_m \end{bmatrix}^{\rm T} </math> 
|-
| '''Alternative notation 1'''<br/>(commas, transpose signs)
| align=center| <math> \begin{bmatrix} x_1, x_2, \dots, x_m \end{bmatrix} </math>
| align=center| <math> \begin{bmatrix} x_1, x_2, \dots, x_m \end{bmatrix}^{\rm T} </math>
|-
| '''Alternative notation 2'''<br/>(commas and semicolons, no transpose signs)
| align=center| <math> \begin{bmatrix} x_1, x_2, \dots, x_m \end{bmatrix} </math>
| align=center| <math> \begin{bmatrix} x_1; x_2; \dots; x_m \end{bmatrix} </math>
|}