Spatial multiplexing is a simple transmission technique for multiple-input multiple-output (MIMO) wireless communication links in which data is multiplexed across the transmit antennas. In Rayleigh fading matrix channels, however, spatial multiplexing with low-complexity linear receivers suffers due to a lack of diversity advantage. This paper proposes multimode antenna selection, which uses a low-rate feedback channel to improve the error rate performance of spatial multiplexing systems with linear receivers. In the proposed technique, both the number of substreams and the mapping of substreams to antennas are dynamically adjusted, for a fixed total data rate, to the channel based on limited feedback from the receiver. Dual-mode selection, where spatial multiplexing or selection diversity is adaptively chosen, dramatically improves the diversity gain achieved. Multimode selection (i.e., allowing any number of substreams to be dynamically selected) provides additional array gain. Various criteria for selecting the number of substreams and the optimal mapping of substreams to transmit antennas are derived. Relationships are made between the selection criteria and the eigenmodes of the channel. A probabilistic analysis of the selection criteria are provided for Rayleigh fading channels. Applications to nonlinear receivers are mentioned. Monte Carlo simulations demonstrate significant performance improvements in independent and identically distributed (i.i.d.) flat-fading Rayleigh matrix channels with minimal feedback.