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Full-Duplex (FD) Amplify-and-Forward (AF) Multiple-Input Multiple-Output (MIMO) relaying has been the focus of several recent studies, due to the potential for achieving a higher spectral efficiency and lower latency, together with inherent processing simplicity. However, when the impact of hardware distortions are considered, such relays suffer from a distortion-amplification loop, due to the inter-dependent nature of the relay transmit signal covariance and the residual self-interference covariance. The aforementioned behavior leads to a significant performance degradation for a system with a low or medium hardware accuracy. In this work, we analyse the relay transfer function as well as the Mean Squared-Error (MSE) performance of an FD-AF MIMO relaying communication, under the impact of collective sources of additive and multiplicative transmit and receive impairments. Building on the performed analysis, an optimization problem is devised to minimize the communication MSE and solved by employing the recently proposed Penalty Dual Decomposition (PDD) framework. The proposed solution converges to a stationary point of the original problem via a sequence of convex quadratic programs (CQP)s, thereby enjoying an acceptable arithmatic complexity as the problem dimensions grow large. Numerical simulations verify the significance of the proposed distortion-aware design and analysis, compared to the common simplified approaches, as the hardware accuracy degrades.