A note on the matrix equation A' LA-L = -K

Matrices W i and N_{i}, which result from application of Krylov's algorithm to the matrices A and B related by A = (B + I)(B - I)^{-1}, are shown to be row equivalent, i.e., N_{i} = M_{i}W_{1} . This result is applied to solution of the Lyapunov matrix equation for discrete-time systems, A'LA - L = -K .