Analysis, design, and implementation of the space vector modulated three-phase to three-phase matrix converter with input power factor correction are presented. The majority of published research results on the matrix converter control is given an overview, and the one, which employs sheous output-voltage and input-current space vector modulation, is systematically reviewed. The modulation algorithm is theoretically derived from the desired average transfer functions, using the indirect transfer function approach. The algorithm is verified through implementation of a 2-kVA experimental matrix converter driving a standard induction motor as a load. The switching frequency is 20 kHz. The modulator is implemented with a digital signal processor. The resultant output voltages and input currents are sinusoidal, practically without low-frequency harmonics. The input power factor is above 0.99 in the whole operating range.