Theorems · Theorem · linear algebra
LinearMap.toSpanSingleton_zero
∀ (R : Type u_1) (M : Type u_4) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M], LinearMap.toSpanSingleton R M 0 = 0
- Defined in
- Mathlib.LinearAlgebra.Span.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement · cited by 10,215
- smul_zeroproof · cited by 665
- LinearMap.ext_ringproof · cited by 152
- LinearMap.toSpanSingletonstatement · cited by 78
- LinearMap.toSpanSingleton_applyproof · cited by 38
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.torsionOf_zeroproof · cited by 2
- LinearMap.toSpanSingleton_eq_zero_iffproof · cited by 0