Theorems · Theorem · linear algebra
Module.Basis.toMatrix_eq_toMatrix_constr
∀ {ι : Type u_1} {R : Type u_5} {M : Type u_6} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(e : Module.Basis ι R M) [inst_3 : Fintype ι] [inst_4 : DecidableEq ι] (v : ι → M),
e.toMatrix v = (LinearMap.toMatrix e e) ((e.constr ℕ) v)- Defined in
- Mathlib.LinearAlgebra.Matrix.Basis
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- LinearEquivstatement · cited by 3,317
- Module.Basisstatement and proof · cited by 1,477
- Matrix.extproof · cited by 540
- Module.Basis.reprproof · cited by 498
Cited by3
Results whose statement or proof uses this declaration.
- Module.Basis.det_compproof · cited by 2
- Module.Basis.is_basis_iff_detproof · cited by 2
- MeasureTheory.Measure.addHaar_parallelepipedproof · cited by 1