The state space may be thought of as a big vector space with each basis element spanning the possible states of one system element (say a memory register or the CAM Angle).

To put it another way, the strings of ones and zeros form the basis for a vector space where our machine state lives. We can write down the state of a QC by writing out a sum like so.

On the basis of the mathematical model of induction machine, simplified mathematical model is deduced, at the same time the theory of DTC is introduced with the concept of space vector.