A matrix inequality associated with bounds on solutions of algebraic Riccati and Lyapunov equations
J. Saniuk, IAN B. RHODES · IEEE Transactions on Automatic Control · 1987
A new proof is presented for the inequality,tr (XY) \leq \parallel X \parallel_{2} \cdot tr Y. This argument is valid under the condition thatYbe real symmetric nonnegative definite;Xmay be any square matrix.