The Algebraic Riccati Matrix Equation for Eigendecomposition of Canonical Forms

The algebraic Riccati matrix equation is used for eigendecomposition of special structured matrices. This is achieved by similarity transformation and then using the algebraic Riccati matrix equation to the triangulation of matrices. The process is the decomposition of matrices into small and specially structured submatrices with low dimensions for easy finding of eigenpairs. Here, we show that previous canonical forms I, II, III, and so on are special cases of the presented method. Numerical and structural examples are included to show the efficiency of the present method.