Theorems · Definition · linear algebra
Pi.basisFun
(R : Type u_2) → (η : Type u_4) → [inst : Semiring R] → [Finite η] → Module.Basis η R (η → R)
The basis on η → R where the ith basis vector is Function.update 0 i 1.
- Defined in
- Mathlib.LinearAlgebra.StdBasis
- Cited by
- 78 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Finitestatement and proof · cited by 3,029
- Module.Basisstatement · cited by 1,477
- LinearEquiv.reflproof · cited by 143
- Module.Basis.ofEquivFunproof · cited by 7
Cited by90
Results whose statement or proof uses this declaration.
- Pi.basisFun_applystatement · cited by 13
- Pi.basisFun_reprstatement · cited by 11
- NumberField.mixedEmbedding.stdBasisproof · cited by 10
- Matrix.stdBasisproof · cited by 10
- Algebra.PreSubmersivePresentation.jacobiMatrix_applyproof · cited by 9
- NumberField.canonicalEmbedding.latticeBasisproof · cited by 7
- Algebra.PreSubmersivePresentation.aevalDifferentialproof · cited by 7
- LDL.lowerInvproof · cited by 6
- dualTensorHom_bijectiveproof · cited by 6
- LinearMap.toMatrix₂'_compl₁₂proof · cited by 6
- Pi.spanSubsetproof · cited by 5
- LinearMap.det_toLin'proof · cited by 4