# Notation and meaning of coordinate system in geometry

I am trying to understand projective geometry to build a 3d scanner, using this text.

http://mesh.brown.edu/byo3d/notes/byo3D.pdf

When describing an idea pinhole camera it says

In the ideal pinhole camera... the center of projection $o$ is at the origin of the world coordinate system, with coordinates $(0; 0; 0) ^t$ , and the point $q$ and the vectors $v1$ and $v2$ are deﬁned as

$[v1 \vert v2 \vert q] = $$\left[\begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]$$$

My questions are what does the notation of $[v1 \vert v2 \vert q]$ mean? Is this a single matrix or is it short hand for defining three column vectors? Also in terms of meaning, why is this the identity matrix?

• It's fairly common to write matrices as a list of column vectors. – Tim Seguine Feb 24 '13 at 19:37

## 1 Answer

From the linked PDF, section 2.2 ("Geometric Representations"):

The $3\times N$ matrix resulting from concatenating $N$ vectors $v_1,\ldots,v_N$ as columns is denoted $\left[v_1\middle|\cdots\middle| v_N\right]$.