Linear receivers are often used to reduce the implementation complexity of multiple antenna systems. In a traditional linear receiver architecture, the receive antennas are used to separate out the codewords sent by each transmit antenna, which can then be decoded individually. Although easy to implement, this approach can be highly sub-optimal when the channel matrix is near singular. In this paper, we develop a new linear architecture that uses the receive antennas to create an effective channel matrix with integer-valued entries. Instead of attempting to recover a transmitted codeword directly, each decoder recovers a different integer combination of the codewords according to the effective channel matrix. If the effective channel is full rank, these linear equations can be digitally solved for the original codewords. By allowing the receiver to equalize the channel to any matrix with integer entries, this scheme can outperform traditional linear architectures such as decorrelators and MMSE receivers while maintaining a similar complexity. Furthermore, in the case where each transmit antenna encodes an independent data stream, the proposed receiver attains the optimal diversity multiplexing tradeoff.