Theorems · Theorem · linear algebra
LinearPMap.neg_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).graph = Submodule.map (LinearMap.id.prodMap (-LinearMap.id)) f.graphThe graph of -f as a pushforward.
- Defined in
- Mathlib.LinearAlgebra.LinearPMap
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Quot.sound
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Ringstatement and proof · cited by 7,463
- Submodulestatement · cited by 7,192
- LinearMap.idstatement and proof · cited by 625
- Submodule.mapstatement and proof · cited by 614
- Submodule.extproof · cited by 204
- LinearPMapstatement and proof · cited by 179
- LinearPMap.domainproof · cited by 167
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