To transform from the world coordinate system to viewing coordinate system you need to perform the following operations. 

a)  Translate the viewing coordinate origin to the world coordinate origin (and hence the scene).

b)  Rotate the axes so that your viewing coordinate system has the same orientation as the world coordinate system.   

While performing such an operation, you are actually performing a change of basis transformation. This again results in another orientation of three mutually perpendicular (linearly independent) unit vectors.