In this paper, a new approach, based on the generalized triangular decomposition (GTD), is proposed for simultaneous wireless information and power transfer (SWIPT) in the spatial domain for a point-to-point multiple-input-multiple-output (MIMO) system. The approach exploits the structure of the GTD to allow the transmitter to use each of the strongest subchannels jointly for energy harvesting and information exchange while the receiver has the ability to harvest energy or decode information from each different received subchannel. An optimal solution is developed in the paper for SWIPT based on GTD that jointly obtains the optimal subchannels assignment and minimizes the total transmitted power for given information rate and energy harvesting constraints under a limited available power per each subchannel at the transmitter. Both the theoretical and numerical results presented in this paper show that our proposed approach significantly outperforms the state of the art spatial domain SWIPT systems based on the singular value decomposition (SVD).