norm — Mathlib

English

The norm on E is defined by ||x|| = sqrt( ||⟪x,x⟫_A|| ).

Русский

Норма на E задаётся как ||x|| = sqrt( ||⟪x,x⟫_A|| ).

LaTeX

$$$\\\\|x\\\\| = \\sqrt{\\\\|\\\\langle x, x \\\\rangle_A\\\\|}$$$

Lean4

/-- The norm associated with a Hilbert C⋆-module. It is not registered as a norm, since a type
might already have a norm defined on it. -/
noncomputable def norm (A : Type*) {E : Type*} [Norm A] [Inner A E] : Norm E where norm x := √‖⟪x, x⟫_A‖

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