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This paper considers a channel estimation scheme for a two-hop non-regenerative MIMO relay system. The scheme has two phases. In the first phase, the source node transmits no signal, the relay transmits a training matrix and the destination estimates the relay-to-destination channel matrix. In the second phase, the source transmits a training matrix, the relay amplifies and forwards with a relay transformation matrix, and the destination estimates the source-to-relay channel matrix. The estimation in each phase is done by the linear minimum mean squared error (LMMSE) method. The correlation in each channel matrix is modeled as a Kronecker product of transmit and receive correlations. Fast algorithms for computing the optimal training matrices at the source and the relay in both phases are developed by using the convex optimization and majorization theory.