Theorems · Theorem · number theory

QuadraticMap.associated_comp

∀ (S : Type u_1) {R : Type u_3} {M : Type u_4} {N : Type u_5} [inst : CommRing R] [inst_1 : AddCommGroup M]
  [inst_2 : Module R M] [inst_3 : AddCommGroup N] [inst_4 : Module R N] [inst_5 : CommSemiring S] [inst_6 : Algebra S R]
  [inst_7 : Module S N] [inst_8 : IsScalarTower S R N] [inst_9 : Invertible 2] (Q : QuadraticMap R M N) {N' : Type u_8}
  [inst_10 : AddCommGroup N'] [inst_11 : Module R N'] (f : N' →ₗ[R] M),
  (QuadraticMap.associatedHom S) (Q.comp f) = LinearMap.compl₁₂ ((QuadraticMap.associatedHom S) Q) f f

Defined in

Mathlib.LinearAlgebra.QuadraticForm.Basic

Cited by

6 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleCommSemiringAlgebraModuleIsScalarTowerInvertibleAddCommGroupModule