Theorems · Theorem · linear algebra
mulLeftLinearMap_zero_eq_zero
∀ {l : Type u_1} {m : Type u_2} (n : Type u_3) (R : Type u_5) {A : Type u_6} [inst : Fintype m] [inst_1 : Semiring R]
[inst_2 : NonUnitalNonAssocSemiring A] [inst_3 : Module R A] [inst_4 : SMulCommClass R A A],
mulLeftLinearMap n R 0 = 0A version of LinearMap.mulLeft_zero_eq_zero for matrix multiplication.
- Defined in
- Mathlib.LinearAlgebra.Matrix.Bilinear
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- SMulCommClassstatement and proof · cited by 1,927
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- LinearMap.extproof · cited by 844
- Matrix.zero_mulproof · cited by 16
- mulLeftLinearMapstatement · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- mulLeftLinearMap_eq_zero_iffproof · cited by 0