We propose two protocols that provide scalable causal consistency for both partitioned and replicated data stores using dependency matrices (DM) and physical clocks. The DM protocol supports basic read and update operations and uses two-dimensional dependency matrices to track dependencies in a client session. It utilizes the transitivity of causality and sparse matrix encoding to keep dependency metadata small and bounded. The DM-Clock protocol extends the DM protocol to support read-only transactions using loosely synchronized physical clocks. We implement the two protocols in Orbe, a distributed key-value store, and valuate them experimentally. Orbe scales out well, incurs relatively small verhead over an eventually consistent key-value store, and outperforms an existing system that uses explicit dependency tracking to provide scalable causal consistency.