dedekind::linear_algebra::IsMatrixSubmoduleLike Concept Reference

Matrices over a ring form at least a submodule-like carrier. More...

Concept definition

template<typename M, typename R>
concept dedekind::linear_algebra::IsMatrixSubmoduleLike =  requires(M a, M b, R s) {
  { a + b } -> std::same_as<M>;
  { a - b } -> std::same_as<M>;
  { -a } -> std::same_as<M>;
  { s * a } -> std::same_as<M>;
  { a * s } -> std::same_as<M>;
}

Detailed Description

Matrices over a ring form at least a submodule-like carrier.

Ring, module, field structure on

matrices.

Operational witness: additive closure, unary negation, and a left scalar action. This is the "at least a submodule" half of the user's claim; the full module proof is the strict IsModule<M, R> specialisation below.