Theorems · Theorem · linear algebra
eval_det_add_X_smul
∀ {n : Type w} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type u_3} [inst_2 : CommRing R]
(A : Matrix n n (Polynomial R)) (M : Matrix n n R),
Polynomial.eval 0 (A + Polynomial.X • M.map ⇑Polynomial.C).det = Polynomial.eval 0 A.det- Cited by
- 2 results in Mathlib
- Foundations
- Depth 126 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.
Cites28
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 and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- Matrixstatement and proof · cited by 4,303
- add_zeroproof · cited by 2,707
- MulZeroClass.mul_zeroproof · cited by 2,091
- Polynomial.Xstatement and proof · cited by 1,639
- map_zeroproof · cited by 1,614
- Polynomial.Cstatement and proof · cited by 1,598
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.derivative_det_one_add_X_smul_auxproof · cited by 1
- Matrix.det_one_add_X_smulproof · cited by 1