Theorems · Theorem · linear algebra
Matrix.mulVec_mulVec
∀ {m : Type u_2} {n : Type u_3} {o : Type u_4} {α : Type v} [inst : NonUnitalSemiring α] [inst_1 : Fintype n]
[inst_2 : Fintype o] (v : o → α) (M : Matrix m n α) (N : Matrix n o α), M.mulVec (N.mulVec v) = (M * N).mulVec v- Defined in
- Mathlib.Data.Matrix.Mul
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 78 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
- NonUnitalSemiringstatement and proof · cited by 339
- Matrix.mulVecstatement · cited by 267
- dotProduct_assocproof · cited by 3
Cited by15
Results whose statement or proof uses this declaration.
- Matrix.mulVecLin_mulproof · cited by 4
- Matrix.posSemidef_conjTranspose_mul_selfproof · cited by 3
- Matrix.PosSemidef.posDef_iff_isUnitproof · cited by 3
- Matrix.toLpLin_mulproof · cited by 2
- RootPairing.GeckConstruction.isNilpotent_eproof · cited by 2
- Matrix.mulVec_cramerproof · cited by 2
- Matrix.inv_mulVec_eq_vecproof · cited by 1
- Matrix.IsHermitian.star_eigenvectorUnitary_mulVecproof · cited by 1
- Matrix.mulVec_surjective_iff_exists_right_inverseproof · cited by 1
- Algebra.discr_mul_isIntegral_mem_adjoinproof · cited by 1
- Matrix.lt_two_mul_of_mul_diagonal_posDef_of_for_le_of_hasEigenproof · cited by 1
- RootPairing.GeckConstruction.ωConjLieSubmodule_eq_top_iffproof · cited by 0