IsSymmetric — Mathlib

English

The canonical endomorphism algebra over a complex Hilbert space is a StarOrderedRing.

Русский

Алгебра эндоморфизмов над комплексным гильбертовым пространством образует StarOrderedRing.

LaTeX

$$StarOrderedRing (H →L[ℂ] H)$$

Lean4

/-- A (not necessarily bounded) operator on an inner product space is symmetric, if for all
`x`, `y`, we have `⟪T x, y⟫ = ⟪x, T y⟫`. -/
def IsSymmetric (T : E →ₗ[𝕜] E) : Prop :=
  ∀ x y, ⟪T x, y⟫ = ⟪x, T y⟫

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