Theorems · Theorem · operator theory

LinearMap.IsSymmetric.apply_eigenvectorBasis

∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {T : E →ₗ[𝕜] E} [inst_3 : FiniteDimensional 𝕜 E] {n : ℕ} (hT : T.IsSymmetric) (hn : Module.finrank 𝕜 E = n)
  (i : Fin n), T ((hT.eigenvectorBasis hn) i) = ↑(hT.eigenvalues hn i) • (hT.eigenvectorBasis hn) i

Defined in

Mathlib.Analysis.InnerProductSpace.Spectrum

Cited by

5 results in Mathlib

Foundations

Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceFiniteDimensional