Theorems · Definition · linear algebra
Matrix.vecMulVec
{m : Type u_2} → {n : Type u_3} → {α : Type v} → [Mul α] → (m → α) → (n → α) → Matrix m n αFor two vectors w and v, vecMulVec w v i j is defined to be w i * v j.
Put another way, vecMulVec w v is exactly replicateCol ι w * replicateRow ι v for
Unique ι; see vecMulVec_eq.
- Defined in
- Mathlib.Data.Matrix.Mul
- Cited by
- 52 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses Quot.sound
- Assumes
- Mul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Matrixstatement · cited by 4,303
- Matrix.ofproof · cited by 336
Cited by53
Results whose statement or proof uses this declaration.
- Matrix.vecMulVec_eqstatement · cited by 7
- LinearMap.toMatrix_innerₛₗ_applystatement · cited by 2
- Matrix.vecMulVec_mulstatement · cited by 1
- Matrix.one_vecMulVecstatement · cited by 1
- Matrix.vecMulVec_onestatement · cited by 1
- Matrix.conjTranspose_vecMulVecstatement · cited by 1
- Matrix.vecMul_vecMulVecstatement · cited by 1
- Matrix.trace_vecMulVecstatement · cited by 1
- InnerProductSpace.symm_toEuclideanLin_rankOnestatement and proof · cited by 1
- Matrix.update_vecMulVecstatement · cited by 1
- vecMulVecBilinproof · cited by 1
- LinearMap.toMatrix_smulRightstatement · cited by 1