Theorems · Theorem · geometry

AffineBasis.isUnit_toMatrix_iff

∀ {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] [inst_5 : DecidableEq ι]
  [Nontrivial k] (p : ι → P), IsUnit (b.toMatrix p) ↔ AffineIndependent k p ∧ affineSpan k (Set.range p) = ⊤

Defined in

Mathlib.LinearAlgebra.AffineSpace.Matrix

Cited by

0 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupAddTorsorRingModuleFintypeDecidableEqNontrivial