Theorems · Theorem · linear algebra
Matrix.mulVecLin_mul
∀ {R : Type u_1} [inst : CommSemiring R] {l : Type u_3} {m : Type u_4} {n : Type u_5} [inst_1 : Fintype n]
[inst_2 : Fintype m] (M : Matrix l m R) (N : Matrix m n R), (M * N).mulVecLin = M.mulVecLin ∘ₗ N.mulVecLin- Defined in
- Mathlib.LinearAlgebra.Matrix.ToLin
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringFintypeFintype
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.
- RingHom.idstatement · cited by 18,349
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- LinearMap.compstatement · cited by 1,642
- LinearMap.extproof · cited by 844
- Matrix.mulVecLinstatement · cited by 38
- Matrix.mulVec_mulVecproof · cited by 15
Cited by4
Results whose statement or proof uses this declaration.
- Matrix.toLin'_mulproof · cited by 8
- Matrix.rank_mul_le_leftproof · cited by 5
- Matrix.rank_mul_le_rightproof · cited by 2
- Matrix.rank_mul_eq_right_of_det_mem_nonZeroDivisorsproof · cited by 2