Theorems · Theorem · linear algebra

LinearMap.IsRefl.ker_eq_bot_iff_ker_flip_eq_bot

∀ {R : Type u_1} {R₁ : Type u_2} {M : Type u_5} {M₁ : Type u_6} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : Module R M] [inst_3 : CommSemiring R₁] [inst_4 : AddCommMonoid M₁] [inst_5 : Module R₁ M₁]
  {I₁ I₂ : R₁ →+* R} {B : M₁ →ₛₗ[I₁] M₁ →ₛₗ[I₂] M}, B.IsRefl → (B.ker = ⊥ ↔ B.flip.ker = ⊥)

Defined in

Mathlib.LinearAlgebra.SesquilinearForm.Basic

Cited by

2 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleCommSemiringAddCommMonoidModule