Theorems · Theorem · linear algebra
Matrix.mul_one
∀ {m : Type u_2} {n : Type u_3} {α : Type v} [inst : NonAssocSemiring α] [inst_1 : Fintype n] [inst_2 : DecidableEq n]
(M : Matrix m n α), M * 1 = M- Defined in
- Mathlib.Data.Matrix.Mul
- Cited by
- 45 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- mul_oneproof · cited by 3,885
- NonAssocSemiringstatement and proof · cited by 805
- Matrix.extproof · cited by 540
- Matrix.mul_diagonalproof · cited by 15
- Matrix.diagonal_oneproof · cited by 13
Cited by45
Results whose statement or proof uses this declaration.
- LinearMap.normDet_eq_norm_det_toMatrix_rangeRestrictproof · cited by 8
- Matrix.Pivot.exists_list_transvec_mul_diagonal_mul_list_transvecproof · cited by 3
- Matrix.nonsing_inv_nonsing_invproof · cited by 3
- Matrix.isRegular_of_isLeftRegular_detproof · cited by 3
- Matrix.zpow_add_oneproof · cited by 3
- LinearMap.toMatrix₂'_compproof · cited by 3
- LinearMap.toMatrix₂_compproof · cited by 3
- Matrix.fromBlocks_eq_of_invertible₁₁proof · cited by 2
- Matrix.Pivot.mul_listTransvecRow_last_col_takeproof · cited by 2
- Matrix.det_kroneckerMapBilinearproof · cited by 2
- Matrix.nonsing_inv_mul_cancel_rightproof · cited by 2
- Matrix.mul_invOf_cancel_rightproof · cited by 2