Simplification of certain linear matrix equations
Stephen Mark Barnett · IEEE Transactions on Automatic Control · 1976
It is shown that in solving the equation\Sigma \alpha_{ij}(A^{T})^{i}PA^{j} = Qfor the symmetric matrixPthe number of linear equations and unknowns call be reduced from\frac{1}{2} n(n + 1)to\frac{1}{2} n(n-1)by introducing a skew symmetric matrix. This generalizes earlier results for Lyapunov matrix equations.