Theorems · Theorem · linear algebra
Polynomial.leadingCoeff_det_X_one_add_C
∀ {n : Type u_1} {α : Type u_2} [inst : DecidableEq n] [inst_1 : Fintype n] [inst_2 : CommRing α] (A : Matrix n n α),
(Polynomial.X • 1 + A.map ⇑Polynomial.C).det.leadingCoeff = 1- Defined in
- Mathlib.LinearAlgebra.Matrix.Polynomial
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 110 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.
Cites24
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
- RingHomstatement · cited by 10,189
- Fintypestatement and proof · cited by 7,736
- Polynomialstatement · cited by 5,681
- Matrixstatement and proof · cited by 4,303
- Nontrivialproof · cited by 2,416
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Fintype.cardproof · cited by 1,386
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.adjugate_mul_distribproof · cited by 3