Theorems · Theorem · linear algebra
Matrix.vec_dotProduct_vec
∀ {m : Type u_2} {n : Type u_3} {R : Type u_1} [inst : AddCommMonoid R] [inst_1 : Mul R] [inst_2 : Fintype m]
[inst_3 : Fintype n] (A B : Matrix m n R), A.vec ⬝ᵥ B.vec = (A.transpose * B).trace- Defined in
- Mathlib.LinearAlgebra.Matrix.Vec
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Finset.sumproof · cited by 5,195
- Matrixstatement and proof · cited by 4,303
- Finset.univproof · cited by 3,473
- Finset.sum_congrproof · cited by 2,323
- Matrix.transposestatement · cited by 389
- dotProductstatement · cited by 194
- Matrix.tracestatement · cited by 114
- Matrix.vecstatement · cited by 27
- Finset.sum_productproof · cited by 27
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.star_vec_dotProduct_vecproof · cited by 1