A skew-symmetric formulation of the algebraic Riccati equation problem

By introducing a set of matrix transformations a new canonical representation in the field of real skew-symmetric matrices is obtained for the algebraic Riccati equation. As a consequence of this reformulation closed-form analytical solutions are derived in
R^{2 \times 2}
or when some special commutativity conditions are fulfilled in the transformed space. The formulation extends the results of [6] to a wider class of Riccati equations.