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In this paper, an analytical framework is developed for the performance analysis of three transmit antenna selection (TAS) strategies for dual-hop multiple-input multiple-output channel-assisted amplify-and-forward (CA-AF) relay networks over Rayleigh fading. The cumulative distribution function of a lower bound of the end-to-end signal-to-noise ratio (SNR) of the optimal TAS strategy is derived and used to obtain the upper bounds of the outage probability and the average symbol error rate (SER). The exact moment generating functions (MGFs) of the end-to-end SNR of two suboptimal TAS strategies are also derived for the ideal CA-AF MIMO relay networks. These MGFs are then used to present accurate and efficient closed-form approximations to evaluate the outage probability and average SER. Numerical and Monte-Carlo simulation results are provided to analyze the performance of the system and to verify the accuracy of our analytical framework.