This thesis presents a systolic algorithm for the SVD of arbitrary complex matrices, based on the cyclic Jacobi method with "parallel ordering". As a basic step in the algorithm, a two-step, two-sided unitary transformation scheme is employed to diagonalize a complex 2 × 2 matrix. The transformations are tailored to the use of CORDIC (COordinate Rotation DIgital Computer) algorithms for high speed arithmetic. The complex SVD array is modeled on the Brent-Luk-VanLoan array for real SVD. An array with O(n\sp2) processors is required to compute the SVD of a n×n matrix in O(n log n) time. An architecture for the complex 2 × 2 processor with an area complexity twice that of a real 2 × 2 processor, is shown to have the best area/time tradeoff for VLSI implementation. Despite the involved nature of computations on complex data, the computation time for the complex SVD array is less than three times that for a real SVD array with a similar CORDIC based implementation.