Spectrum sensing is a key function of cognitive radios and is used to determine whether a primary user is present in the channel or not. Many approaches have been proposed when both primary user and secondary user employ a single antenna. Recently several techniques have also been proposed assuming that the the secondary user employs multiple antennas. In this paper, we formulate and solve the generalized likelihood ratio test (GLRT) for spectrum sensing when both primary user transmitter and the secondary user receiver are equipped with multiple antennas. We do not assume any prior information about the channel statistics or the primary user's signal structure. Two cases are considered when the secondary user is aware of the energy of the noise and when it is not. The final test statistics derived from GLRT are based on the eigenvalues of the sample covariance matrix. Through analysis we exhibit the role of the eigenvalues in characterizing the signal+noise and noise subspaces in the received data. Simulation results are presented in terms of the receiver operating characteristics and detection probabilities for several cases of interest.