Theorems · Theorem · linear algebra
Module.Basis.unitsSMul_apply
∀ {ι : Type u_1} {R : Type u_2} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
{v : Module.Basis ι R M} {w : ι → Rˣ} (i : ι), (v.unitsSMul w) i = w i • v i- Defined in
- Mathlib.LinearAlgebra.Basis.SMul
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Unitsstatement and proof · cited by 2,804
- Module.Basisstatement and proof · cited by 1,477
- Eq.geproof · cited by 375
- Module.Basis.linearIndependentproof · cited by 54
- Module.Basis.span_eqproof · cited by 44
- Module.Basis.unitsSMulstatement · cited by 9
- Module.Basis.mk_applyproof · cited by 9
- LinearIndependent.units_smulproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- Module.Basis.toMatrix_unitsSMulproof · cited by 2
- Module.Basis.adjustToOrientation_apply_eq_or_eq_negproof · cited by 2
- Module.Basis.isUnitSMul_applyproof · cited by 1