Theorems · Theorem · linear algebra

LinearMap.IsPerfectCompl.isCompl_right

∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  [inst_3 : AddCommGroup N] [inst_4 : Module R N] {p : M →ₗ[R] N →ₗ[R] R} [inst_5 : p.IsPerfPair] {U : Submodule R M}
  {V : Submodule R N}, p.IsPerfectCompl U V → IsCompl V (Submodule.map (↑p.flip.toPerfPair.symm) U.dualAnnihilator)

Defined in

Mathlib.LinearAlgebra.PerfectPairing.Basic

Cited by

2 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleLinearMap.IsPerfPair