Theorems · Inductive type · linear algebra

LinearMap.IsPerfectCompl

{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) → [p.IsPerfPair] → Submodule R M → Submodule R N → Prop

Given a perfect pairing p between M and N, we say a pair of submodules U in M and V in N are perfectly complementary w.r.t. p if their dual annihilators are complementary, using p to identify M and N with dual spaces.

Defined in

Mathlib.LinearAlgebra.PerfectPairing.Basic

Cited by

10 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleLinearMap.IsPerfPair