Scaling of general quadratic matrix equations

A scaling framework for general quadratic algebraic matrix equations is presented. All algebraic quadratic equations can be considered as special cases of a single generalized algebraic quadratic matrix equation (GQME). Hence, the paper is focused on the analysis and solution of the scaling problem of that GQME. The presented scaling method is based on the assignment of predetermined values of the coefficients and the unknown matrices of the GQME. The proposed framework is independent of any numerical method and therefore its use is general. Implementations are presented for the special case of matrix algebraic Riccati equations (AREs). Some new results of matrix algebraic identities considering Kronecker and Hadamard products are also reported.