Theorems · Theorem · linear algebra
Matrix.zero_mul
∀ {l : Type u_1} {m : Type u_2} {n : Type u_3} {α : Type v} [inst : NonUnitalNonAssocSemiring α] [inst_1 : Fintype m]
(M : Matrix m n α), 0 * M = 0- Defined in
- Mathlib.Data.Matrix.Mul
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 57 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.
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- Matrix.extproof · cited by 540
- zero_dotProductproof · cited by 9
Cited by17
Results whose statement or proof uses this declaration.
- Matrix.J_squaredproof · cited by 3
- Matrix.fromBlocks_eq_of_invertible₁₁proof · cited by 2
- Matrix.addMonoidHomMulRightproof · cited by 2
- Matrix.charpoly_mul_comm'proof · cited by 2
- Matrix.TransvectionStruct.mul_sumInl_toMatrix_prodproof · cited by 1
- mulLeftLinearMap_zero_eq_zeroproof · cited by 1
- Matrix.TransvectionStruct.sumInl_toMatrix_prod_mulproof · cited by 1
- Matrix.toBlock_inverse_eq_zeroproof · cited by 1
- CStarMatrix.zero_mulproof · cited by 0
- LieAlgebra.Orthogonal.jb_transformproof · cited by 0
- Matrix.updateRow_zero_mul_updateCol_zeroproof · cited by 0
- LieAlgebra.Orthogonal.pb_invproof · cited by 0