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PIERS Online
Vol. 3
No. 5
2007
pp: 629-632On the Gersgorin Theorem Applied To Radar PolarimetryE. Luneburg, Andreas Danklmayer, and Wolfgang-Martin Boerner doi:10.2529/PIERS061006084930 Downloads: 775 Abstract:This contribution is concerned with the mathematical formulation and theoretical background of the Gersgorin theory in the context of Radar Polarimetry. Named after its founder Semian A. Gersgorin the Gersgorin theorem basically states that there are certain regions in the complex plane that can be derived from any n × n complex matrix by rather simple arithmetic operations. These regions are containing more information, specifically its eigenvalues lying within or at the boundaries of circles, where the radii are obtained by the deleted absolute row and/or column sums of the respective n × n complex matrices.References:1. Horn, R. A. and C. R. Johnson, Matrix Analysis, Cambridge University Press, New York, 1985. 2. Varga, R. S., Gersgorin and his Circles, Springer, 2004. 3. Luneburg, E. and W.-M. Boerner, "Statistical aspects of radar polarimetry," Fields, Networks, Computational Methods, and Systems in Modern Electrodynamics, P. Russer, M. Mongiardo (Editors), A Tribute to Leopold B. Felsen (the Proceedings of the Symposium on Fields, Networks and Computation: A Modern View of Engineering Electrodynamics, June 01-02, 2004, Technical University of Munich, Springer-Verlag Berlin-Heidelberg-New York, 2004. |
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