nnnorm_algebraMap — Mathlib

English

For x in 𝕜, the nonnegative norm of algebraMap 𝕜 𝕜' x equals the product of the nonnegative norms.

Русский

Для x в 𝕜 неделимый подмассива: nnnorm(algebraMap 𝕜 𝕜' x) = nnnorm(x) · nnnorm(1).

LaTeX

$$$\\|\\mathrm{algebraMap}_{\\mathbb{K} \\to \\mathbb{K}'}(x)\\|_+ = \\|x\\|_+ \\cdot \\|1_{\\mathbb{K}'}\\|_+$$$

Lean4

theorem nnnorm_algebraMap (x : 𝕜) : ‖algebraMap 𝕜 𝕜' x‖₊ = ‖x‖₊ * ‖(1 : 𝕜')‖₊ :=
  Subtype.ext <| norm_algebraMap 𝕜' x

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