For massive multiple-input multiple-output (MIMO) communication systems, simple linear detectors such as zero forcing (ZF) and minimum mean square error (MMSE) can achieve near-optimal detection performance with reduced computational complexity. However, such linear detectors always involve complicated matrix inversion, which will suffer from high computational overhead in the practical implementation. Due to the massive parallel-processing and efficient hardware-implementation nature, the neural network has become a promising approach to signal processing for the future wireless communications. In this paper, we first propose an efficient neural network to calculate the pseudo-inverses for any type of matrices based on the improved Newton's method, termed as the PINN. Through detailed analysis and derivation, the linear massive MIMO detectors are mapped on PINNs, which can take full advantage of the research achievements of neural networks in both algorithms and hardwares. Furthermore, an improved limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) quasi-Newton method is studied as the learning algorithm of PINNs to achieve a better performance/complexity trade-off. Simulation results finally validate the efficiency of the proposed scheme.