Theorems · Definition · linear algebra
Matrix.single
{m : Type u_2} →
{n : Type u_3} → {α : Type u_7} → [DecidableEq m] → [DecidableEq n] → [Zero α] → m → n → α → Matrix m n αsingle i j a is the matrix with a in the i-th row, j-th column,
and zeroes elsewhere.
- Defined in
- Mathlib.Data.Matrix.Basis
- Cited by
- 129 results in Mathlib
- Foundations
- Depth 14 from the axioms, rests on 73 definitions · uses Quot.sound
- Assumes
- DecidableEqDecidableEqZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Matrixstatement · cited by 4,303
- Matrix.ofproof · cited by 336
Cited by136
Results whose statement or proof uses this declaration.
- Matrix.transvectionproof · cited by 24
- Matrix.single_apply_of_nestatement · cited by 16
- Matrix.single_apply_samestatement · cited by 16
- MatrixModCat.toModuleCatObjproof · cited by 7
- Matrix.mul_single_apply_samestatement · cited by 7
- RingCon.ofMatrixproof · cited by 6
- Matrix.matrix_eq_sum_singlestatement · cited by 6
- Matrix.single_eq_of_single_singlestatement · cited by 6
- Matrix.single_zerostatement · cited by 6
- Matrix.center_eq_scalar_imageproof · cited by 6
- MatrixEquivTensor.invFunproof · cited by 6
- matPolyEquiv_coeff_applyproof · cited by 5