Theorems · Theorem · linear algebra
LinearMap.transvection.comp_of_left_eq
∀ {R : Type u_1} {V : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid V] [inst_2 : Module R V]
{f : Module.Dual R V} {v w : V},
f w = 0 → LinearMap.transvection f v ∘ₗ LinearMap.transvection f w = LinearMap.transvection f (v + w)- Defined in
- Mathlib.LinearAlgebra.Transvection.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement · cited by 10,215
- LinearMap.compstatement · cited by 1,642
- LinearMap.extproof · cited by 844
- Module.Dualstatement and proof · cited by 583
- LinearMap.transvectionstatement and proof · cited by 32
- LinearMap.transvection.comp_of_left_eq_applyproof · cited by 3
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