Theorems · Definition · linear algebra
Matrix.mulVecLin
{R : Type u_1} →
[inst : CommSemiring R] → {m : Type u_4} → {n : Type u_5} → [Fintype n] → Matrix m n R → (n → R) →ₗ[R] m → RMatrix.mulVec M as a linear map.
Note this is a special case of Matrix.mulVecBilin.
- Defined in
- Mathlib.LinearAlgebra.Matrix.ToLin
- Cited by
- 38 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringFintype
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.
- DFunLike.coeproof · cited by 62,936
- 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
- Matrix.mulVecBilinproof · cited by 3
Cited by40
Results whose statement or proof uses this declaration.
- Matrix.rankproof · cited by 48
- LinearMap.toMatrix'proof · cited by 46
- Matrix.rank_mul_le_leftproof · cited by 5
- Matrix.mulVecLin_mulstatement · cited by 4
- Matrix.mulVecLin_submatrixstatement · cited by 3
- Matrix.toLin'_apply'statement · cited by 3
- Matrix.rank_transposeproof · cited by 3
- Matrix.PosSemidef.posDef_iff_isUnitproof · cited by 3
- Matrix.rank_le_card_widthproof · cited by 3
- Matrix.rank_mul_eq_right_of_det_mem_nonZeroDivisorsproof · cited by 2
- Matrix.rank_mul_le_rightproof · cited by 2
- Matrix.mulVecLin_onestatement · cited by 2