Theorems · Definition · geometry

AffineBasis.basisOf

{ι : Type u_1} →
  {k : Type u_5} →
    {V : Type u_6} →
      {P : Type u_7} →
        [inst : AddCommGroup V] →
          [inst_1 : AddTorsor V P] →
            [inst_2 : Ring k] → [inst_3 : Module k V] → AffineBasis ι k P → (i : ι) → Module.Basis { j // j ≠ i } k V

Given an affine basis for an affine space P, if we single out one member of the family, we obtain a linear basis for the model space V. The linear basis corresponding to the singled-out member i : ι is indexed by {j : ι // j ≠ i} and its jth element is b j -ᵥ b i. (See basisOf_apply.)

Defined in

Mathlib.LinearAlgebra.AffineSpace.Basis

Cited by

11 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupAddTorsorRingModule