Theorems · Theorem · linear algebra
LinearMap.BilinForm.ext
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
{B D : LinearMap.BilinForm R M}, (∀ (x y : M), (B x) y = (D x) y) → B = D- Defined in
- Mathlib.LinearAlgebra.BilinearForm.Basic
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- LinearMap.BilinFormstatement and proof · cited by 501
- LinearMap.ext₂proof · cited by 17
Cited by22
Results whose statement or proof uses this declaration.
- LinearMap.BilinForm.ext_of_isSymmproof · cited by 3
- LieIdeal.isSolvable_of_killingForm_apply_lie_eq_zeroproof · cited by 2
- LieModule.traceForm_eq_sum_finrank_nsmulproof · cited by 2
- LinearMap.BilinForm.isAdjointPair_unique_of_nondegenerateproof · cited by 1
- LieSubmodule.traceForm_eq_of_le_idealizerproof · cited by 1
- LinearMap.BilinForm.isSymm_iff_flipproof · cited by 1
- traceForm_nondegenerate_tfaeproof · cited by 1
- LieModule.traceForm_eq_zero_of_isNilpotentproof · cited by 1
- LinearMap.BilinForm.baseChange_eq_zero_iffproof · cited by 0
- LinearMap.BilinForm.flip_flipproof · cited by 0
- LinearMap.BilinForm.compLeft_idproof · cited by 0
- LinearMap.BilinForm.compRight_idproof · cited by 0