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Theorems · Theorem · operator theory

LinearMap.IsSymmetric.id

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E],
  LinearMap.id.IsSymmetric
Defined in
Mathlib.Analysis.InnerProductSpace.Symmetric
Cited by
3 results in Mathlib
Foundations
Depth 47 from the axioms · uses propext, Quot.sound
Assumes
RCLikeSeminormedAddCommGroupInnerProductSpace
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Around this declaration

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

LinearMap.isSymmetric_adjoint_comp_self · cited by 11LinearMap.isSymmetric_adj…LinearMap.isPositive_one · cited by 5LinearMap.isPositive_oneLinearMap.isSymmetric_self_comp_adjoint · cited by 0LinearMap.isSymmetric_sel…InnerProductSpace · cited by 3523InnerProductSpaceRCLike · cited by 2829RCLikeSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupLinearMap.id · cited by 625LinearMap.idLinearMap.IsSymmetric · cited by 121LinearMap.IsSymmetricIsSymmetric.idCITED BYCITES

Cites5

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Cited by3

Results whose statement or proof uses this declaration.