Theorems · Theorem · linear algebra

exteriorPower.basis_coord

∀ (R : Type u_1) {M : Type u_3} (n : ℕ) [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  {I : Type u_5} [inst_3 : LinearOrder I] (b : Module.Basis I R M) (s : ↑(Set.powersetCard I n)),
  (Module.Basis.exteriorPower n b).coord s = exteriorPower.ιMultiDual R n b s

If b is a basis of M indexed by a linearly ordered type I and B is the corresponding basis of the nth exterior power of M, indexed by the set of finsets s of I of cardinality n, then the coordinate function of B at s is the linear form on the nth exterior power defined by b and s in exteriorPower.ιMultiDual.

Defined in

Mathlib.LinearAlgebra.ExteriorPower.Basis

Cited by

1 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleLinearOrder