Theorems · Theorem · operator theory

eigenvalue_pos_of_pos

∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {μ : ℝ} {T : E →ₗ[𝕜] E}, Module.End.HasEigenvalue T ↑μ → (∀ (x : E), 0 < RCLike.re (inner 𝕜 x (T x))) → 0 < μ

Defined in

Mathlib.Analysis.InnerProductSpace.Spectrum

Cited by

0 results in Mathlib

Foundations

Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpace