Theorems · Definition · linear algebra
LinearMap.BilinMap
(R : Type u_2) →
[inst : CommSemiring R] →
(M : Type u_5) →
(Nₗ : Type u_8) →
[inst_1 : AddCommMonoid M] → [inst_2 : AddCommMonoid Nₗ] → [Module R M] → [Module R Nₗ] → Type (max u_8 u_5)A shorthand for the type of R-bilinear Nₗ-valued maps on M.
- Defined in
- Mathlib.LinearAlgebra.BilinearMap
- Cited by
- 85 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- RingHom.idproof · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapproof · cited by 10,215
Cited by107
Results whose statement or proof uses this declaration.
- LinearMap.BilinFormproof · cited by 501
- LinearMap.BilinMap.toQuadraticMapstatement and proof · cited by 53
- QuadraticMap.associatedstatement · cited by 34
- QuadraticMap.associatedHomstatement · cited by 29
- QuadraticMap.polarBilinstatement · cited by 25
- LinearMap.BilinForm.tmulstatement and proof · cited by 9
- QuadraticMap.associated_eq_self_applystatement · cited by 7
- QuadraticMap.toBilinstatement · cited by 6
- QuadraticForm.associated_tmulstatement and proof · cited by 6
- QuadraticMap.associated_compstatement · cited by 6
- QuadraticMap.polar_smul_leftproof · cited by 5
- LinearEquiv.congrRight₂statement · cited by 5