Simplification of the Lyapunov matrix equation A_{T}PA - P = -Q

It is shown that in solving for the symmetric matrix P the number of linear equations and unknowns can be reduced from \frac{1}{2}n(n + 1) to \frac{1}{2}n(n - 1) by introducing a skew-symmetric matrix. This corresponds to an earlier result for the equation A_{1}^{T}P_{1} + P_{1}A = -Q .