  Modern research in code generators for dense linear algebra computations has
shown the ability to produce optimized code with a performance which compares
and often exceeds the one of state-of-the-art implementations by domain
experts. However, the underlying infrastructure is often developed in isolation
making the interconnection of logically combinable systems complicated if not
impossible. In this paper, we propose to leverage MLIR as a unifying compiler
infrastructure for the optimization of dense linear algebra operations. We
propose a new MLIR dialect for expressing linear algebraic computations
including matrix properties to enable high-level algorithmic transformations.
The integration of this new dialect in MLIR enables end-to-end compilation of
matrix computations via conversion to existing lower-level dialects already
provided by the framework.
