There is an implicit initial user space in place at the start of every SVG drawing. This initial user space defines how the canvas is mapped onto the viewport. By establishing a new viewport, you implicitly also establish a new viewport space and thus a new initial user space. Transformations To change the current user space coordinate system, you define a transformation which defines how to transform coordinates from the new user space coordinate system into the previous coordinate system. Mathematically, the transformation is represented by a transformation matrix which maps coordinates in the new user space coordinate system into the previous coordinate system.
Transformation matrices define the mathematical mapping from one coordinate space into another.
Whenever a new transformation is provided, a new CTM is calculated by the following formula. Transformations alter coordinate systems, not objects. All objects defined outside the scope of a transformation are unchanged by the transformation. All objects defined within the scope of a transformation will be drawn in the transformed coordinate system. All coordinates used within the scope the transformation are specified in the transformed coordinate system.