Bounds for solutions of the discrete algebraic Lyapunov equation

A family of sharp, arbitrarily tight upper and lower matrix bounds far solu tions of the discrete algebraic Lyapunov are presented. The lower bounds ar e tighter than previously. known ones. Unlike the majority of previously kn own upper bounds? those derived here have no restrictions on their applicab ility. Upper and lower bounds for individual eigenvalues and for the trace of the solution are found using the new matrix bounds. Sharp trace hounds n ot derivable from the matrix bounds are also presented.