Theorems · Theorem · linear algebra
Matrix.row_eq_zero_of_commute_single
∀ {n : Type u_3} {α : Type u_7} [inst : DecidableEq n] [inst_1 : Fintype n] [inst_2 : Semiring α] {i j k : n}
{M : Matrix n n α}, Commute (Matrix.single i j 1) M → k ≠ j → M j k = 0- Defined in
- Mathlib.Data.Matrix.Basis
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintypeSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- one_mulproof · cited by 2,841
- Commutestatement and proof · cited by 639
- Matrix.singlestatement and proof · cited by 129
- Matrix.ext_iffproof · cited by 18
- Matrix.mul_single_apply_of_neproof · cited by 4
- Matrix.single_mul_apply_sameproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.mem_range_scalar_of_commute_singleproof · cited by 2