Theorems · Theorem · linear algebra
LinearPMap.inverse_graph
∀ {R : Type u_1} [inst : Ring R] {E : Type u_4} [inst_1 : AddCommGroup E] [inst_2 : Module R E] {F : Type u_5}
[inst_3 : AddCommGroup F] [inst_4 : Module R F] {f : E →ₗ.[R] F},
f.toFun.ker = ⊥ → f.inverse.graph = Submodule.map (↑(LinearEquiv.prodComm R E F)) f.graph- Defined in
- Mathlib.LinearAlgebra.LinearPMap
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- Bot.botstatement and proof · cited by 4,720
- LinearEquiv.toLinearMapstatement and proof · cited by 1,171
- LinearMap.kerstatement and proof · cited by 848
- Submodule.mapstatement and proof · cited by 614
- LinearPMapstatement and proof · cited by 179
- LinearPMap.domainstatement · cited by 167
- LinearPMap.graphstatement and proof · cited by 39
Cited by4
Results whose statement or proof uses this declaration.
- LinearPMap.closure_inverse_graphproof · cited by 2
- LinearPMap.mem_inverse_graphproof · cited by 1
- LinearPMap.inverse_isClosable_iffproof · cited by 1
- LinearPMap.inverse_closed_iffproof · cited by 0