Theorems · Theorem · linear algebra

Lagrange.sum_nodalWeight_mul_inv_sub_ne_zero

∀ {F : Type u_1} [inst : Field F] {ι : Type u_2} [inst_1 : DecidableEq ι] {s : Finset ι} {v : ι → F} {x : F},
  Set.InjOn v ↑s → (∀ i ∈ s, x ≠ v i) → s.Nonempty → ∑ i ∈ s, Lagrange.nodalWeight s v i * (x - v i)⁻¹ ≠ 0

Defined in

Mathlib.LinearAlgebra.Lagrange

Cited by

0 results in Mathlib

Foundations

Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldDecidableEq