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In this letter, we propose multi-antenna based spectrum sensing methods for cognitive radios (CRs) using the generalized likelihood ratio test (GLRT) paradigm. The proposed methods utilize the eigenvalues of the sample covariance matrix of the received signal vector from multiple antennas, taking advantage of the fact that in practice, the primary user signals to be detected will either occupy a subspace of dimension strictly smaller than the dimension of the observation space, or have a non-white spatial spectrum. These methods do not require prior knowledge of the primary user signals, or the channels from the primary users to the CR. By making different assumptions on the availability of the white noise power value at the CR receiver, we derive two algorithms that are shown to outperform the standard energy detector.