Theorems · Theorem · linear algebra
Matrix.derivative_det_one_add_X_smul_aux
∀ {R : Type u} [inst : CommRing R] {n : ℕ} (M : Matrix (Fin n) (Fin n) R),
Polynomial.eval 0 (Polynomial.derivative (1 + Polynomial.X • M.map ⇑Polynomial.C).det) = M.trace- Cited by
- 1 results in Mathlib
- Foundations
- Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites59
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.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Matrixstatement and proof · cited by 4,303
- mul_oneproof · cited by 3,885
- Finset.univproof · cited by 3,473
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.derivative_det_one_add_X_smulproof · cited by 0