Theorems · Theorem · linear algebra
LinearMap.IsSymm.nondegenerate_restrict_of_isCompl_ker
∀ {R : Type u_1} {M : Type u_5} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
{B : M →ₗ[R] M →ₗ[R] R}, B.IsSymm → ∀ {W : Submodule R M}, IsCompl W B.ker → (B.domRestrict₁₂ W W).Nondegenerate- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- add_zeroproof · cited by 2,707
- map_addproof · cited by 964
- LinearMap.kerstatement and proof · cited by 848
- LinearMap.extproof · cited by 844
- Submodule.subtypeproof · cited by 480
Cited by1
Results whose statement or proof uses this declaration.
- RootPairing.rootForm_restrict_nondegenerate_of_isAnisotropicproof · cited by 0