Theorems · Theorem · linear algebra
Matrix.vecMulVec_eq
∀ {m : Type u_2} {n : Type u_3} {α : Type v} (ι : Type u_6) [inst : Mul α] [inst_1 : AddCommMonoid α]
[inst_2 : Unique ι] (w : m → α) (v : n → α), Matrix.vecMulVec w v = Matrix.replicateCol ι w * Matrix.replicateRow ι v- Defined in
- Mathlib.LinearAlgebra.Matrix.RowCol
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MulAddCommMonoidUnique
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumproof · cited by 5,195
- Matrixstatement · cited by 4,303
- one_smulproof · cited by 1,374
- Matrix.extproof · cited by 540
- Uniquestatement and proof · cited by 400
- Finset.sum_constproof · cited by 254
- Finset.card_singletonproof · cited by 144
- Finset.univ_uniqueproof · cited by 94
- Matrix.vecMulVecstatement · cited by 52
- Matrix.replicateColstatement · cited by 42
- Matrix.replicateRowstatement · cited by 40
Cited by7
Results whose statement or proof uses this declaration.
- Matrix.trace_vecMulVecproof · cited by 1
- Matrix.charpoly_vecMulVecproof · cited by 0
- Matrix.rank_vecMulVecproof · cited by 0
- InnerProductSpace.toMatrix_rankOneproof · cited by 0
- Matrix.posSemidef_vecMulVec_star_selfproof · cited by 0
- Matrix.posSemidef_vecMulVec_self_starproof · cited by 0
- Matrix.rank_vecMulVec_leproof · cited by 0