Theorems · Theorem · operator theory

LinearMap.IsSymmetric.eigenvectorBasis.congr_simp

∀ {𝕜 : Type u_3} [inst : RCLike 𝕜] {E : Type u_4} [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {T T_1 : E →ₗ[𝕜] E} (e_T : T = T_1) [inst_3 : FiniteDimensional 𝕜 E] {n : ℕ} (hT : T.IsSymmetric)
  (hn : Module.finrank 𝕜 E = n), hT.eigenvectorBasis hn = ⋯.eigenvectorBasis hn

Defined in: Mathlib.Analysis.InnerProductSpace.Spectrum
Cited by: 0 results in Mathlib
Foundations: Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: RCLike NormedAddCommGroup InnerProductSpace FiniteDimensional

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RingHom.idstatement and proof · cited by 18,349
NormedAddCommGroupstatement and proof · cited by 15,752
LinearMapstatement and proof · cited by 10,215
InnerProductSpacestatement and proof · cited by 3,523
RCLikestatement and proof · cited by 2,829
FiniteDimensionalstatement and proof · cited by 1,854
Module.finrankstatement and proof · cited by 1,770
OrthonormalBasisstatement · cited by 188
LinearMap.IsSymmetricstatement and proof · cited by 121
LinearMap.IsSymmetric.eigenvectorBasisstatement and proof · cited by 11

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