Theorems · Definition · linear algebra
LinearMap.BilinForm.restrict
{R : Type u_1} →
{M : Type u_2} →
[inst : CommSemiring R] →
[inst_1 : AddCommMonoid M] →
[inst_2 : Module R M] → LinearMap.BilinForm R M → (W : Submodule R M) → LinearMap.BilinForm R ↥WThe restriction of a bilinear form on a submodule.
- Defined in
- Mathlib.LinearAlgebra.BilinearForm.Basic
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement and proof · cited by 7,192
- LinearMap.BilinFormstatement and proof · cited by 501
- LinearMap.domRestrict₁₂proof · cited by 9
Cited by24
Results whose statement or proof uses this declaration.
- LinearMap.BilinForm.isCompl_orthogonal_of_restrict_nondegeneratestatement and proof · cited by 3
- LinearMap.BilinForm.restrict_applystatement and proof · cited by 3
- LinearMap.BilinForm.restrict_nondegenerate_iff_isCompl_orthogonalstatement and proof · cited by 2
- LinearMap.BilinForm.eq_top_of_restrict_nondegenerate_of_orthogonal_eq_botstatement and proof · cited by 2
- LieDerivation.IsKilling.killingForm_restrict_range_adstatement and proof · cited by 2
- LieAlgebra.IsKilling.restrict_killingForm_eq_sumstatement · cited by 1
- LinearMap.BilinForm.inf_orthogonal_self_le_ker_restrictstatement · cited by 1
- LinearMap.BilinForm.nondegenerate_restrict_of_disjoint_orthogonalstatement · cited by 1
- LieIdeal.killingForm_eqstatement · cited by 1
- LieSubmodule.traceForm_eq_of_le_idealizerstatement · cited by 1
- LieAlgebra.restrict_killingFormstatement · cited by 1
- LinearMap.BilinForm.ker_restrict_eq_of_codisjointstatement and proof · cited by 1