Theorems · Theorem · linear algebra
Module.Basis.sum_equivFun
∀ {ι : Type u_1} {R : Type u_3} {M : Type u_6} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[inst_3 : Fintype ι] (b : Module.Basis ι R M) (u : M), ∑ i, b.equivFun u i • b i = u- Defined in
- Mathlib.LinearAlgebra.Basis.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
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 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
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement · cited by 5,195
- Finset.univstatement · cited by 3,473
- LinearEquivstatement · cited by 3,317
- Module.Basisstatement and proof · cited by 1,477
- Module.Basis.equivFunstatement and proof · cited by 88
- LinearEquiv.symm_apply_applyproof · cited by 78
Cited by5
Results whose statement or proof uses this declaration.
- Module.Basis.sum_reprproof · cited by 29
- Module.Basis.opNNNorm_leproof · cited by 2
- Algebra.traceMatrix_of_basis_mulVecproof · cited by 2
- WeierstrassCurve.Affine.CoordinateRing.exists_smul_basis_eqproof · cited by 2
- LinearMap.transvection.eq_id_of_finrank_le_oneproof · cited by 0