The core component of a cognitive radio is its detector. When a device is equipped with multiple antennas, the detection method is usually based on an eigenvalue analysis. This paper explores the performance of the most common largest eigenvalue detector, for the case of a narrowband temporally white signal and calibrated receiver noise. In contrast to popular Gaussian assumption, our performance bounds are valid for any signal and noise that belong to the wide class of sub-Gaussian random processes. Moreover, the results are given in closed-form for any finite number of observations and antennas, in contrary to the widespread asymptotic analysis approach.