Theorems · Theorem · linear algebra
Polynomial.coeff_det_X_add_C_card
∀ {n : Type u_1} {α : Type u_2} [inst : DecidableEq n] [inst_1 : Fintype n] [inst_2 : CommRing α] (A B : Matrix n n α),
(Polynomial.X • A.map ⇑Polynomial.C + B.map ⇑Polynomial.C).det.coeff (Fintype.card n) = A.det- Defined in
- Mathlib.LinearAlgebra.Matrix.Polynomial
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintypeCommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites41
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
- CommRingstatement and proof · cited by 17,173
- Semiringproof · cited by 13,802
- RingHomstatement · cited by 10,189
- Fintypestatement and proof · cited by 7,736
- Polynomialstatement and proof · cited by 5,681
- Finset.sumproof · cited by 5,195
- Matrixstatement and proof · cited by 4,303
- mul_oneproof · cited by 3,885
- Finset.univproof · cited by 3,473
- Unitsproof · cited by 2,804
- add_zeroproof · cited by 2,707
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.leadingCoeff_det_X_one_add_Cproof · cited by 1