Example systems and processes use three-phase vector mutual inductance analysis to detect zero-crossing (ZC) locations of back-electromotive force (BEMF) of an electric motor and to detect its commutation points during start-up or low-speed operation. For each sector of rotation of the rotor, two pairs of three-phase vectors are applied, along with current for the corresponding driving phase. The first pair is alternately applied to move the rotor, and the mutual inductances resulting from such application are compared to detect the zero-crossing (ZC) location in the BEMF of the electric motor in that sector. The second pair is then alternately applied within the same sector to continue to move the rotor, and the mutual inductances from such application are compared to detect the commutation point of the electric motor in that sector. The process may be repeated for each successive sector, changing the driving current at each new sector.