Theorems · Theorem · operator theory

LinearMap.IsSymmetric.smul

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {c : 𝕜}, (starRingEnd 𝕜) c = c → ∀ {T : E →ₗ[𝕜] E}, T.IsSymmetric → (c • T).IsSymmetric

Defined in

Mathlib.Analysis.InnerProductSpace.Symmetric

Cited by

2 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Quot.sound

Assumes

RCLikeSeminormedAddCommGroupInnerProductSpace