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Simultaneous matrix equations are first given for solving the problems of scattering by many homogeneous gyrotropic cylinders of different kinds. The numerical results are illustrated for two circular ferrite cylinders, elliptic and circular ferrite cylinders, two parallel linear arrays of circular ferrite cylinders, and a circular array of twelve circular plasma cylinders around a magnetic current source. It is indicated that a sharp main lobe of the linear arrays illuminated by an -plane wave can be veered by a reversal of the applied static magnetic field, and that with a cyclic change of the dc magnetic fields applied to the circular array one can rotate the radiation pattern having a single big lobe with suppressed side lobes. Some discussions for electronic lobe switching and electronic scanning by gyrotropic cylinders are given. The effects of interactions among the cylinders are also discussed.