Theorems · Theorem · operator theory

LinearMap.IsSymmetric.exists_eigenvalues_eq

∀ {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) {μ : 𝕜},
  Module.End.HasEigenvalue T μ → ∃ i, ↑(hT.eigenvalues hn i) = μ

Defined in

Mathlib.Analysis.InnerProductSpace.Spectrum

Cited by

1 results in Mathlib

Foundations

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

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceFiniteDimensional