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We propose new low complexity opportunistic relaying strategies for multiple-antenna relay networks. Assuming that a source communicates with a destination, both equipped with M antennas, assisted by K single-antenna relay terminals using an amplify-and-forward half-duplex protocol, we propose a new transmission strategy which employs linear zero-forcing transmission and reception. Integrated with this transmission strategy, we propose two low complexity opportunistic relay selection algorithms, referred to as the Maximum Sum Rate Relay Selection (MSR) and Greedy Semi-Orthogonal Relay Selection (GSO) algorithms, which select only a few very important relays to share the total power. For the GSO algorithm, we present a theoretical analysis of the sum capacity as K grows large, which is shown to be M/2 log log K + O(1). This result is also shown to coincide with a fundamental cut-set upper bound on the sum capacity of MIMO networks with opportunistic relaying which we derive; thereby establishing a new exact scaling law for such networks, as well as demonstrating the asymptotic optimality of our proposed low complexity approach. Our numerical studies also indicate that our proposed opportunistic relaying techniques yield significant capacity benefits over the conventional approach without opportunistic selection, even when the number of relays is not large.