Theorems · Theorem · linear algebra

Module.Basis.det_reindex

∀ {R : Type u_1} [inst : CommRing R] {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M] {ι : Type u_4}
  [inst_3 : DecidableEq ι] [inst_4 : Fintype ι] {ι' : Type u_6} [inst_5 : Fintype ι'] [inst_6 : DecidableEq ι']
  (b : Module.Basis ι R M) (v : ι' → M) (e : ι ≃ ι'), (b.reindex e).det v = b.det (v ∘ ⇑e)

Defined in

Mathlib.LinearAlgebra.Determinant

Cited by

2 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleDecidableEqFintypeFintypeDecidableEq