dedekind::linear_algebra::HasMultiplicativeInverse Concept Reference

A matrix carrier with a closed-form inverse operation. More...

Concept definition

template<typename M>
concept dedekind::linear_algebra::HasMultiplicativeInverse =  requires(const M& a) {
  { a.inverse() };
}

Detailed Description

A matrix carrier with a closed-form inverse operation.

Weaker than dedekind.algebra:IsDivisionRing<M>, which demands full ring closure (+, -, *) alongside a.inverse(). For n ≥ 2 square-matrix carriers over a field, IsDivisionRing<M> does not hold: Mₙ(F) has zero divisors (e.g. [[1,0],[0,0]]·[[0,0],[0,1]] = 0). The only matrix-flavoured carriers for which IsDivisionRing fires cleanly are M₁(F) ≅ F and genuine division algebras (quaternions, ...).