Eigenvalue bounds in the Lyapunov and Riccati matrix equations

Two related theorems of Strang [1] are extended to provide upper and lower bounds on the eigenvalues of the Lyapunov and Riccati matrices, given by
Q=AB^{H}+BA
and
R=AB^{H}+BA+2AHA
, where
A
and
H
are Hermitian, positive definite, complex matrices. We discuss inversion to obtain eigenvalue bounds on the matrix
A
for the usual case in which
Q , R
, and
H
are known.