Identity Transformation

The simplest transformation you can perform on a vector is none at all. The identity transformation is like multiplying by one.

\[\M{I}=\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ \end{bmatrix}\] \[\begin{array}{ccccccccccl} w_x &=& v_x\cdot 1 &+& v_y\cdot 0 &+& v_z\cdot 0 &+& v_w\cdot 0 &=& v_x \\ w_y &=& v_x\cdot 0 &+& v_y\cdot 1 &+& v_z\cdot 0 &+& v_w\cdot 0 &=& v_y \\ w_z &=& v_x\cdot 0 &+& v_y\cdot 0 &+& v_z\cdot 1 &+& v_w\cdot 0 &=& v_z \\ w_w &=& v_x\cdot 0 &+& v_y\cdot 0 &+& v_z\cdot 0 &+& v_w\cdot 1 &=& v_w \\ \end{array}\]