Theorems · Theorem · linear algebra
Matrix.toMvPolynomial_mul
∀ {m : Type u_1} {n : Type u_2} {o : Type u_3} {R : Type u_4} [inst : Fintype n] [inst_1 : Fintype o]
[inst_2 : CommSemiring R] (M : Matrix m n R) (N : Matrix n o R) (i : m),
(M * N).toMvPolynomial i = (MvPolynomial.bind₁ N.toMvPolynomial) (M.toMvPolynomial i)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeFintypeCommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Finsetproof · cited by 13,712
- AddCommMonoidproof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Fintypestatement and proof · cited by 7,736
- Finsuppstatement · cited by 5,255
- Finset.sumproof · cited by 5,195
- Algebra.algebraMapproof · cited by 4,706
- Matrixstatement and proof · cited by 4,303
- Finset.univproof · cited by 3,473
- AlgHomstatement · cited by 3,236
- zero_addproof · cited by 2,366
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.toMvPolynomial_compproof · cited by 2