Eigenvalue decomposition (EVD) is a widely-used factorization tool to perform principal component analysis, and has been employed for dimensionality reduction and pattern recognition in many scientific and engineering applications, such as image processing, text mining and wireless communications. EVD is considered computationally expensive, and as software implementations have not been able to meet the performance requirements of many real-time applications, the use of reconfigurable computing technology has shown promise in accelerating this type of computation. In this paper, we present an efficient FPGA-based double-precision floating-point architecture for EVD, which can efficiently analyze large-scale matrices. Our experimental results using an FPGA-based hybrid acceleration system indicate the efficiency of our novel array architecture, with dimension-dependent speedups over an optimized software implementation that range from 1.5x to 15.45x in terms of computation time.