dedekind::linear_algebra::IsTransposeDualPair Concept Reference

V and Covec are dual under transpose: V → Covec and Covec → V, with both round-trips returning the original type. More...

Concept definition

template<typename V, typename Covec>
concept dedekind::linear_algebra::IsTransposeDualPair = 
    HasTranspose<V> && HasTranspose<Covec> &&
    std::same_as<std::remove_cvref_t<decltype(std::declval<V>().transpose())>,
                 std::remove_cvref_t<Covec>> &&
    std::same_as<
        std::remove_cvref_t<decltype(std::declval<Covec>().transpose())>,
        std::remove_cvref_t<V>>

Detailed Description

V and Covec are dual under transpose: V → Covec and Covec → V, with both round-trips returning the original type.

Formalises the column/row duality. transpose is the canonical isomorphism V ↔ V* in finite dimension; double-transpose returns to the original carrier on each side. Together the pair (V, Covec) carries the same ℤ/2 action as HasInvolutiveTranspose, but spelled across two distinct orientations.