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Simplification of certain linear matrix equations

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1 Author(s)
Barnett, S. ; University of Bradford, Bradford, West Yorks, England

It is shown that in solving the equation \Sigma \alpha _{ij}(A^{T})^{i}PA^{j} = Q for the symmetric matrix P the 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.

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Automatic Control, IEEE Transactions on  (Volume:21 ,  Issue: 1 )