Lower bounds on the solution of Lyapunov matrix and algebraic Riccati equations

In this note various lower bounds for all the eigenvalues of the solution matrix
K
of the Lyapunov matrix equation are established. A special case of this result is a generalization of that presented in [1]-[3], where lower bounds for the maximum and minimum eigenvalues of
K
are given. Moreover, the approach used here enables one to establish various lower bounds for some of the (largest) eigenvalues of the solution matrix of the algebraic Riccati equation.