Theorems · Theorem · functional analysis

ContinuousLinearMap.inverse_eq_ringInverse

∀ {R : Type u_1} {M : Type u_2} {M₂ : Type u_3} [inst : TopologicalSpace M] [inst_1 : TopologicalSpace M₂]
  [inst_2 : Semiring R] [inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : AddCommMonoid M₂]
  [inst_6 : Module R M₂] (e : M ≃L[R] M₂) (f : M →L[R] M₂), f.inverse = Ring.inverse (↑e.symm ∘SL f) ∘SL ↑e.symm

The function ContinuousLinearEquiv.inverse can be written in terms of Ring.inverse for the ring of self-maps of the domain.

Defined in

Mathlib.Topology.Algebra.Module.Equiv

Cited by

2 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceSemiringAddCommMonoidModuleAddCommMonoidModule