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Spectrum sensing for cognitive radio allows a secondary user to detect spectrum `holes` and to opportunistically exploit this space for unlicensed communication. Blind spectrum sensing has the advantage that it does not require any knowledge of the transmitted signal, the channel or the noise-power, which are usually unknown at the receiver. In this study, the simulation and performance results for the maximum`minimum-eigenvalue and energy-minimum-eigenvalue sensing methods are presented for the Nakagami-m fading channel. The simulation and performance results are presented for the maximum-eigenvalue-to-trace method and the arithmetic-to-geometric-mean method together with the analytical expressions for the threshold, probability of detection and probability of false alarm. In addition, another algorithm, maximum-eigenvalue-geometric-mean is proposed and is investigated in terms of the analytical and simulation results for Nakagami-m fading channels. Improved performance is shown compared to the other schemes when the number of samples is decreased and when the number of cooperating users is increased such that the ratio of the latter to the former is positive and less than unity. Analytical expressions are also presented. The eigenvalue detection methods exhibit good performance in noisy environments and are matched by their bounds.