Theorems · Theorem · linear algebra
Matrix.replicateRow_mul_replicateCol_apply
∀ {m : Type u_2} {α : Type v} {ι : Type u_6} [inst : Fintype m] [inst_1 : Mul α] [inst_2 : AddCommMonoid α]
(v w : m → α) (i j : ι), (Matrix.replicateRow ι v * Matrix.replicateCol ι w) i j = v ⬝ᵥ w- Defined in
- Mathlib.LinearAlgebra.Matrix.RowCol
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- FintypeMulAddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- dotProductstatement · cited by 194
- Matrix.replicateColstatement · cited by 42
- Matrix.replicateRowstatement · cited by 40
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.det_one_add_replicateCol_mul_replicateRowproof · cited by 0