This is the conclusion of the previous section: in a constant magnetic field B along z axis the transverse magnetization M rotates around this axis in clockwise direction with angular frequency ω. If the observer were rotating around the same axis in  clockwise direction with angular frequency  Ω, M it would appear to her or him  rotating with angular frequency  ω - Ω. Specifically, if the observer were rotating around the same axis in
clockwise direction with angular frequency ω, the transverse magnetization M would appear to her or him stationary.
This can be expressed mathematically in the following way:
* Let (x, y, z) the Cartesian coordinate system of the laboratory (or stationary) frame of reference, and
* (x&prime;, y&prime;, z&prime;) = (x&prime;, y&prime;, z) be a Cartesian coordinate system that is rotating around the z axis of the laboratory frame of reference with angular frequency Ω. This is called the rotating frame of reference. Physical variables in this frame of reference will be denoted by a prime.
Obviously:
What is M&prime;(t)? Expressing the argument at the beginning of this section in a mathematical way: