We present a methodology for exploiting shared-memory parallelism within matrix computations by expressing linear algebra algorithms as directed acyclic graphs. Our solution involves a separation of concerns that completely hides the exploitation of parallelism from the code that implements the linear algebra algorithms. This approach to the problem is fundamentally different since we also address the issue of programmability instead of strictly focusing on parallelization. Using the separation of concerns, we present a framework for analyzing and developing scheduling algorithms and heuristics for this problem domain. As such, we develop a theory and practice of scheduling concepts for matrix computations.