Theorems · Theorem · number theory

AbsoluteValue.iSup_abv_linearMap_apply_le

∀ {K : Type u_1} [inst : Field K] {ι : Type u_2} {ι' : Type u_3} [inst_1 : Fintype ι] [Finite ι']
  (v : AbsoluteValue K ℝ) (A : ι' × ι → K) (x : ι → K),
  ⨆ j, v (∑ i, A (j, i) * x i) ≤ (↑(Nat.card ι) * ⨆ ji, v (A ji)) * ⨆ i, v (x i)

Defined in

Mathlib.NumberTheory.Height.MvPolynomial

Cited by

1 results in Mathlib

Foundations

Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFintypeFinite