With dedicated semantics it becomes possible for a compiler to optimize things explicitly rather than implicitly. It's sort of equivalent to how a language with

With dedicated semantics it becomes possible for a compiler to optimize things explicitly rather than implicitly. It's sort of equivalent to how a language without generics or inheritance can't perform certain optimizations (like inlining method calls) because the compiler isn't aware of those semantics in the first place. The overhead of BLAS is significant for small matrices. However, a compiler can tell if matrices are small at compile time (or JIT time) and inline the expressions which presents enormous speed gains. It can also make judgement calls about when to use sparse or dense arrays but that's a bit trickier. Compilers can do this without knowing that matrices or linear algebra exist, but it usually takes PGO which can be difficult to use. Iirc there's a linear algebra library for Julia that can beat the LAPACK backends for small matrices, which is a pretty big deal. There are also classes of optimizations like SIMD that don't just depend on matrix size but the target platform, which may not be the platform the software was compiled on. The way to do this is with function multiversioning but not all compilers/languages support it, this is kind of a classic usecase for a JIT compiler. One of the reasons Eigen is great is because it can use template semantics to make these optimizations at compile time. It's just slightly annoying in how it harms compile times.