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Mathematical Problems in Engineering
Volume 2013, Article ID 176389, 7 pages
Research Article

The Algebraic Riccati Matrix Equation for Eigendecomposition of Canonical Forms

1Department of Structural Engineering, Shabestar Branch, Islamic Azad University, Shabestar, Iran
2Marand Faculty of Engineering, University of Tabriz, Tabriz, Iran

Received 10 December 2012; Accepted 7 February 2013

Academic Editor: Sebastian Anita

Copyright © 2013 M. Nouri and S. Talatahari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.