Theorems · Theorem · linear algebra

AlternatingMap.map_insertNth

∀ {R : Type u_1} {M : Type u_2} {N : Type u_4} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : AddCommGroup N]
  [inst_3 : Module R M] [inst_4 : Module R N] {n : ℕ} (f : M [⋀^Fin (n + 1)]→ₗ[R] N) (p : Fin (n + 1)) (x : M)
  (v : Fin n → M), f (p.insertNth x v) = (-1) ^ ↑p • f (Matrix.vecCons x v)

If f is a (n + 1)-multilinear alternating map, x is an element of the domain, and v is an n-vector, then the value of f at v with x inserted at the pth place equals (-1) ^ p times the value of f at v with x prepended.

Defined in

Mathlib.LinearAlgebra.Alternating.Uncurry.Fin

Cited by

3 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupAddCommGroupModuleModule