Theorems · Theorem · linear algebra

Module.Ray.linearEquiv_smul_eq_map

∀ {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] (e : M ≃ₗ[R] M) (v : Module.Ray R M), e • v = (Module.Ray.map e) v

The action via LinearEquiv.apply_distribMulAction corresponds to Module.Ray.map.

Defined in

Mathlib.LinearAlgebra.Ray

Cited by

0 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringPartialOrderIsStrictOrderedRingAddCommMonoidModule