AbstractBy introducing a set of matrix transformations, the algebraic Riccati equation (ARE) is converted into a ‘dual’ matrix quadratic equation (DARE) where the unknown belongs to the field of skew‐symmetric matrices. As a consequence of this reformulation for a matrix space Rnxnthe system ofn(n+ 1)/2 coupled quadratic equations associated to ARE is shown to be equivalent to another system ofn(n‐1)/2 coupled quadratic equations. An efficient computational algorithm is given for solving the dual Riccati equation and closed form analytical solutions of ARE are derived for the case in whichn=2 or when some special, but non‐trivial, commutativity conditions are fulfilled in the transfor