reApplyInnerSelf — Mathlib

English

For any operator T and vector x, the real bilinear form reApplyInnerSelf satisfies T.reApplyInnerSelf x = Re⟪T x, x⟫.

Русский

Для оператора T и вектора x справедливо: T.reApplyInnerSelf x = Re⟪T x, x⟫.

LaTeX

$$T.reApplyInnerSelf x = Re⟪T x, x⟫$$

Lean4

/-- Extract a real bilinear form from an operator `T`,
by taking the pairing `fun x ↦ re ⟪T x, x⟫`. -/
def reApplyInnerSelf (T : E →L[𝕜] E) (x : E) : ℝ :=
  re ⟪T x, x⟫

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