Theorems · Theorem · linear algebra
Matrix.stdBasis_eq_single
∀ (R : Type u_1) {m : Type u_2} {n : Type u_3} [inst : Fintype m] [inst_1 : Finite n] [inst_2 : Semiring R] (i : m)
(j : n) [inst_3 : DecidableEq m] [inst_4 : DecidableEq n], (Matrix.stdBasis R m n) (i, j) = Matrix.single i j 1- Defined in
- Mathlib.LinearAlgebra.Matrix.StdBasis
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Semiringstatement and proof · cited by 13,802
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- Finitestatement and proof · cited by 3,029
- Module.Basisstatement · cited by 1,477
- Pi.singleproof · cited by 518
- Matrix.ofproof · cited by 336
- Matrix.singlestatement · cited by 129
- Pi.basisFunproof · cited by 78
- Equiv.sigmaEquivProdproof · cited by 47
- Module.Basis.coe_reindexproof · cited by 27
Cited by3
Results whose statement or proof uses this declaration.
- Module.Basis.linearMap_apply_applyproof · cited by 2
- AlgHom.mulLeftRightMatrix.comp_invproof · cited by 1
- AlgHom.mulLeftRightMatrix.inv_compproof · cited by 1