Theorems · Theorem · linear algebra

Orientation.map_apply

∀ {R : Type u_1} [inst : CommSemiring R] [inst_1 : PartialOrder R] [inst_2 : IsStrictOrderedRing R] {M : Type u_2}
  [inst_3 : AddCommMonoid M] [inst_4 : Module R M] {N : Type u_3} [inst_5 : AddCommMonoid N] [inst_6 : Module R N]
  (ι : Type u_4) (e : M ≃ₗ[R] N) (v : M [⋀^ι]→ₗ[R] R) (hv : v ≠ 0),
  (Orientation.map ι e) (rayOfNeZero R v hv) = rayOfNeZero R (v.compLinearMap ↑e.symm) ⋯

Defined in

Mathlib.LinearAlgebra.Orientation

Cited by

2 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringPartialOrderIsStrictOrderedRingAddCommMonoidModuleAddCommMonoidModule