We analyze the performance of amplify-and-forward (AF) multiple-input multiple-output (MIMO) cooperative networks over independent but not identically distributed Nakagami-$m$ fading channels. Specifically, we consider an AF MIMO relay network where the source deploys the transmit antenna selection scheme to communicate with the destination through the help of a relay. We derive closed-form approximations for outage probability (OP) and symbol error probability (SEP). Moreover, asymptotically tight approximations for OP and SEP have been obtained to facilitate insights on how fading parameters affect the performance. Our analytical results are verified by Monte-Carlo simulations for respective scenarios.