Mathlib Map

Theorems · Theorem · linear algebra

LinearMap.IsPosSemidef.isSymm

∀ {R : Type u_1} {M : Type u_5} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {I₁ : R →+* R}
  [inst_3 : LE R] {B : M →ₛₗ[I₁] M →ₗ[R] R}, B.IsPosSemidef → B.IsSymm
Defined in
Mathlib.LinearAlgebra.SesquilinearForm.Basic
Cited by
2 results in Mathlib
Foundations
Depth 33 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringAddCommMonoidModuleLE
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

LinearMap.isPosSemidef_def · cited by 3LinearMap.isPosSemidef_defLinearMap.IsPosSemidef.add · cited by 1IsPosSemidef.addModule · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idAddCommMonoid · cited by 12281AddCommMonoidCommSemiring · cited by 10911CommSemiringLinearMap · cited by 10215LinearMapRingHom · cited by 10189RingHomLinearMap.IsSymm · cited by 48LinearMap.IsSymmLinearMap.IsPosSemidef · cited by 8LinearMap.IsPosSemidefIsPosSemidef.isSymmCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.