Theorems · Theorem · operator theory

LinearMap.trace_eq_sum_inner

∀ {𝕜 : Type u_1} {E : Type u_2} {ι : Type u_3} [inst : RCLike 𝕜] [inst_1 : Fintype ι] [inst_2 : NormedAddCommGroup E]
  [inst_3 : InnerProductSpace 𝕜 E] (T : E →ₗ[𝕜] E) (b : OrthonormalBasis ι 𝕜 E),
  (LinearMap.trace 𝕜 E) T = ∑ i, inner 𝕜 (b i) (T (b i))

Defined in

Mathlib.Analysis.InnerProductSpace.Trace

Cited by

1 results in Mathlib

Foundations

Depth 230 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeFintypeNormedAddCommGroupInnerProductSpace