Theorems · Theorem · linear algebra
Matrix.mulVec_sub
∀ {m : Type u_2} {n : Type u_3} {α : Type v} [inst : NonUnitalNonAssocRing α] [inst_1 : Fintype n] (A : Matrix m n α)
(x y : n → α), A.mulVec (x - y) = A.mulVec x - A.mulVec y- Defined in
- Mathlib.Data.Matrix.Mul
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonUnitalNonAssocRingFintype
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
- NonUnitalNonAssocRingstatement and proof · cited by 354
- Matrix.mulVecstatement · cited by 267
- dotProduct_subproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Matrix.PosDef.isUnitproof · cited by 4
- Matrix.mulVec_injective_of_det_mem_nonZeroDivisorsproof · cited by 3
- Int.Matrix.exists_ne_zero_int_vec_norm_leproof · cited by 1