In this paper we investigate low complexity joint transmit and receive antenna selection (JTRAS) algorithms for wireless spatial multiplexing (SM) systems. Unlike the conventional JTRAS algorithms that mainly use capacity maximization based criterion, we propose a general method for joint transmit and receive antenna selection according to different selection criteria, including minimum mean square error (MMSE), maximum minimum signal-to-interference-plus-noise ratio (SINR), and maximum capacity. The proposed method for different selection criteria is based on the calculation of matrix inverse and the recursive matrix inverse update is developed to reduce computational complexity. Extensive simulation results show that our algorithms perform very close to the optimal exhaustive search algorithms and better than or equivalent to the suboptimal algorithms in terms of bit error rate (BER) and ergodic capacity in both the uncorrelated and highly correlated MIMO channels, while the computational complexity is much lower than the optimal algorithms.