Theorems · Theorem · linear algebra

exteriorPower.finrank_eq

∀ (R : Type u_1) {M : Type u_3} (n : ℕ) [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  [Nontrivial R] [Module.Free R M] [Module.Finite R M], Module.finrank R ↥(⋀[R]^n M) = (Module.finrank R M).choose n

If R is non-trivial and M is finite free of rank r, then the nth exterior power of M is of finrank Nat.choose r n.

Defined in

Mathlib.LinearAlgebra.ExteriorPower.Basis

Cited by

1 results in Mathlib

Foundations

Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleNontrivialModule.FreeModule.Finite