Theorems · Theorem · linear algebra
Module.Basis.coord_apply
∀ {ι : Type u_10} {R : Type u_11} {M : Type u_12} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(b : Module.Basis ι R M) (i : ι) (x : M), (b.coord i) x = (b.repr x) i- Defined in
- Mathlib.LinearAlgebra.Basis.Defs
- Cited by
- 49 results in Mathlib
- Foundations
- Depth 76 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.
Cites11
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
- Finsuppstatement · cited by 5,255
- LinearEquivstatement · cited by 3,317
- Module.Basisstatement and proof · cited by 1,477
- Module.Basis.reprstatement · cited by 498
- Module.Basis.coordstatement and proof · cited by 64
Cited by49
Results whose statement or proof uses this declaration.
- LinearMap.BilinForm.apply_dualBasis_leftproof · cited by 5
- IsLocalFrameOn.coeff_sum_eqproof · cited by 5
- Module.End.mem_center_iffproof · cited by 4
- exteriorPower.ιMultiDual_apply_diagproof · cited by 3
- exteriorPower.ιMultiDual_apply_nondiagproof · cited by 3
- Bundle.Trivialization.localFrameCoeff_apply_of_mem_baseSetproof · cited by 2
- LinearEquiv.mem_dilatransvections_iff_rankproof · cited by 2
- Module.Basis.sumQuot_repr_inrproof · cited by 2
- Module.Basis.flag_le_ker_coord_iffproof · cited by 2
- LinearMap.trace_eq_contract_of_basisproof · cited by 2
- LieAlgebra.Basis.symm_baseSuppproof · cited by 2
- IsLocalFrameOn.coeff_congrproof · cited by 2