Optical processing of information holds great promise for addressing many challenges facing the field of computing. However, integrated photonic processors are typically limited by the physical size of the processing units and the energy consumption of high-speed analog-to-digital conversion. In this paper, we demonstrate an integrated, coherent approach to processing temporally multiplexed optical signals using a modular dot-product unit cell to address these challenges. We use these unit cells to demonstrate multiply-accumulate operations on real- and complex-valued inputs using coherent detection and temporal integration. We then extend this to computing the covariance between stochastic bit streams, which can be used to estimate correlation between data streams in the optical domain. Finally, we demonstrate a path to scaling up our platform to enable general matrix-matrix operations. Our approach has the potential to enable highly efficient and scalable optical computing on-chip for a broad variety of AI applications.