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Optimal transmit/receive diversity (TRD) is one of the most important configurations for wireless multiple-input multiple-output (MIMO) systems, due to its good performance and ease of implementation. Though investigated intensively, the performance of optimal TRD in general correlated fading with cochannel interference is still not well understood. Since the optimal TRD's output instantaneous signal-to-interference-plus-noise ratio (SINR) is equal to the largest sample eigenvalue of a quadratic form involving signal and interference channel matrices, directly determining the probability density function (pdf) of this eigenvalue has been a prevailing approach in the literature. Given the nonlinearity involved in the quadratic form, however, finding such a pdf is not simple except for some special channel conditions. In this paper, we formulate the problem, in a totally different framework, as testing the positive-definiteness of a random matrix whereby the theory of matrix-variate distributions can be invoked to obtain exact solutions in terms of special functions. The solutions are very general including most of existing results as a special case and allowing for the correlation structures of both signal and interferers to be arbitrary at both transmitter and receiver ends. Numerical results are presented to validate the theoretical analysis.