Theorems · Theorem · geometry

AffineBasis.toMatrix_vecMul_coords

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

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

Defined in

Mathlib.LinearAlgebra.AffineSpace.Matrix

Cited by

2 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupAddTorsorRingModuleFintype