In this paper, concise upper and lower matrix bounds for the solution of the continuous Riccati equation are presented. These results are new and the lower matrix bound is better than the previously reported one. According to these estimates, all the bounds for eigenvalues, trace, determinant, etc, can then be defined. A lower matrix bound and eigenvalue bounds of the solution of the continuous algebraic Lyapunov equation are also determined. The main feature of this paper is that all the present results are new and are sharper than the majority of those reported in the literature. Finally, we give an illustrative example to make comparisons for the present schemes and existing bounds.