Theorems · Theorem · geometry

AffineBasis.toMatrix_inv_vecMul_toMatrix

∀ {ι : Type u₁} {k : Type u₂} {V : Type u₃} {P : Type u₄} [inst : AddCommGroup V] [inst_1 : AddTorsor V P]
  [inst_2 : CommRing k] [inst_3 : Module k V] [inst_4 : DecidableEq ι] [inst_5 : Fintype ι] (b b₂ : AffineBasis ι k P)
  (x : P), Matrix.vecMul (b.coords x) (b.toMatrix ⇑b₂)⁻¹ = b₂.coords x

A change of basis formula for barycentric coordinates. See also AffineBasis.toMatrix_vecMul_coords.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Matrix

Cited by

1 results in Mathlib

Foundations

Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupAddTorsorCommRingModuleDecidableEqFintype