Theorems · Theorem · number theory

QuadraticMap.two_nsmul_associated

∀ (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),
  2 • (QuadraticMap.associatedHom S) Q = Q.polarBilin

Twice the associated bilinear map of Q is the same as the polar of Q.

Defined in

Mathlib.LinearAlgebra.QuadraticForm.Basic

Cited by

2 results in Mathlib

Foundations

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

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleCommSemiringAlgebraModuleIsScalarTowerInvertible