Since the state transformation of the shift register contents is a linear operation, a matrix equation describing it can be given. Continuing with the example of the 10-long generator, if we define and by:

then the action of the shift register can be readily described by the equation

where is the entire vector after **n** time steps.
If the vector has been given some initial
set of values, then we have,

etc., and in general,

As an aside, note that , or , the identity matrix.