Theorems · Theorem · operator theory

LinearMap.IsSymmetric.eigenvalues_antitone

∀ {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),
  Antitone (hT.eigenvalues hn)

Eigenvalues are sorted in decreasing order.

Defined in

Mathlib.Analysis.InnerProductSpace.Spectrum

Cited by

3 results in Mathlib

Foundations

Depth 256 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceFiniteDimensional