Theorems · Theorem · linear algebra
eval_det
∀ {n : Type w} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type u_3} [inst_2 : CommRing R]
(M : Matrix n n (Polynomial R)) (r : R),
Polynomial.eval r M.det = (Polynomial.eval ((Matrix.scalar n) r) (matPolyEquiv M)).det- Cited by
- 3 results in Mathlib
- Foundations
- Depth 125 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.
Cites17
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
- RingHom.idproof · cited by 18,349
- 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
- Matrixstatement and proof · cited by 4,303
- AlgEquivstatement · cited by 1,681
- Polynomial.evalstatement and proof · cited by 796
- Matrix.detstatement and proof · cited by 665
- Matrix.extproof · cited by 540
- Matrix.scalarstatement and proof · cited by 62
Cited by3
Results whose statement or proof uses this declaration.
- Matrix.det_eq_sign_charpoly_coeffproof · cited by 5
- eval_det_add_X_smulproof · cited by 2
- Matrix.det_one_add_smulproof · cited by 1