<p>It is not necessarily affine. An affine matrix in homogeneous coordinates has a form like:</p>

<p>$$\begin{bmatrix} a_{11} &amp; a_{12} &amp; a_{13} \\ a_{21} &amp; a_{22} &amp; a_{23} \\ 0 &amp; 0 &amp; 1 \end{bmatrix}$$</p>

<p>(assuming you use a column vector convention). Here, the upper-left 2&times;2 submatrix is the linear part, and $(a_{13}, a_{23})$ is the translation vector of the affine transform.</p>

<p>If the lower row of the matrix has some values other than $[0, 0, 1]$, then it is in general a projective transform, not an affine one.</p>

CC BY-SA 3.0
2016-04-30T22:00:59.013Z
2016-04-30T22:00:59.013Z
Nathan Reed
<p>We have a matrix      </p>

<p>$$\begin{bmatrix} a_{11} &amp; a_{12} &amp; a_{13} \\ a_{21} &amp; a_{22} &amp; a_{23} \\ a_{31} &amp; a_{32} &amp; a_{33} \end{bmatrix}$$</p>

<p>This matrix represents a transformation in homogeneous coordinates.
My question is whether the above matrix is affine or not and an example too for this.                  </p>

<transformations><affine-transformations><matrix>
Affine Transformation
Sharmishtha
# Affine Transformation

(Asked by: username_0 on 2016-04-30)

We have a matrix

$$\begin{bmatrix} a\_{11} & a\_{12} & a\_{13} \\ a\_{21} & a\_{22} & a\_{23} \\ a\_{31} & a\_{32} & a\_{33} \end{bmatrix}$$

This matrix represents a transformation in homogeneous coordinates.
My question is whether the above matrix is affine or not and an example too for this.

**Tags:** transformations, affine-transformations, matrix


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## 1 answers

### Answer by username_1 on 2016-04-30. Score: 4 | Accepted answer

It is not necessarily affine. An affine matrix in homogeneous coordinates has a form like:

$$\begin{bmatrix} a\_{11} & a\_{12} & a\_{13} \\ a\_{21} & a\_{22} & a\_{23} \\ 0 & 0 & 1 \end{bmatrix}$$

(assuming you use a column vector convention). Here, the upper-left 2×2 submatrix is the linear part, and $(a\_{13}, a\_{23})$ is the translation vector of the affine transform.

If the lower row of the matrix has some values other than $[0, 0, 1]$, then it is in general a projective transform, not an affine one.


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