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Theorems · Definition · linear algebra

LinearMap.BilinForm.IsRefl

{R : Type u_1} →
  {M : Type u_2} →
    [inst : CommSemiring R] → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → LinearMap.BilinForm R M → Prop

The proposition that a bilinear form is reflexive

Defined in
Mathlib.LinearAlgebra.BilinearForm.Properties
Cited by
30 results in Mathlib
Foundations
Depth 34 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringAddCommMonoidModule

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

LinearMap.BilinForm.isCompl_orthogonal_of_restrict_nondegenerate · cited by 3BilinForm.isCompl_orthogo…LieAlgebra.InvariantForm.orthogonal_isCompl_toSubmodule · cited by 3InvariantForm.orthogonal_…LinearMap.BilinForm.orthogonal_top_eq_ker · cited by 3BilinForm.orthogonal_top_…LinearMap.BilinForm.finrank_add_finrank_orthogonal · cited by 2BilinForm.finrank_add_fin…LinearMap.BilinForm.isCompl_orthogonal_iff_disjoint · cited by 2BilinForm.isCompl_orthogo…LinearMap.BilinForm.restrict_nondegenerate_iff_isCompl_orthogonal · cited by 2BilinForm.restrict_nondeg…LinearMap.BilinForm.IsRefl.eq_iff · cited by 2IsRefl.eq_iffLinearMap.BilinForm.eq_top_of_restrict_nondegenerate_of_orthogonal_eq_bot · cited by 2BilinForm.eq_top_of_restr…LinearMap.BilinForm.inf_orthogonal_self_le_ker_restrict · cited by 1BilinForm.inf_orthogonal_…LieAlgebra.InvariantForm.atomistic · cited by 1InvariantForm.atomisticLieAlgebra.InvariantForm.orthogonal_isCompl · cited by 1InvariantForm.orthogonal_…LinearMap.BilinForm.le_orthogonal_orthogonal · cited by 1BilinForm.le_orthogonal_o…LinearMap.BilinForm.nondegenerate_restrict_of_disjoint_orthogonal · cited by 1BilinForm.nondegenerate_r…LinearMap.BilinForm.orthogonal_orthogonal · cited by 1BilinForm.orthogonal_orth…LinearMap.BilinForm.IsRefl.eq_zero · cited by 1IsRefl.eq_zeroModule · cited by 20661ModuleAddCommMonoid · cited by 12281AddCommMonoidCommSemiring · cited by 10911CommSemiringLinearMap.BilinForm · cited by 501LinearMap.BilinFormLinearMap.IsRefl · cited by 16LinearMap.IsReflBilinForm.IsReflCITED BYCITES

Cites5

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Cited by30

Results whose statement or proof uses this declaration.