Theorems · Definition · global analysis

VectorField.pullback

(𝕜 : Type u_1) →
  [inst : NontriviallyNormedField 𝕜] →
    {E : Type u_2} →
      [inst_1 : NormedAddCommGroup E] →
        [NormedSpace 𝕜 E] →
          {F : Type u_3} → [inst_3 : NormedAddCommGroup F] → [NormedSpace 𝕜 F] → (E → F) → (F → F) → E → E

The pullback of a vector field under a function, defined as (f^* V) (x) = Df(x)^{-1} (V (f x)). If Df(x) is not invertible, we use the junk value 0.

Defined in

Mathlib.Analysis.Calculus.VectorField

Cited by

7 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace