Theorems · Theorem · linear algebra
Matrix.det_eq_sign_charpoly_coeff
∀ {R : Type u} [inst : CommRing R] {n : Type v} [inst_1 : DecidableEq n] [inst_2 : Fintype n] (M : Matrix n n R),
M.det = (-1) ^ Fintype.card n * M.charpoly.coeff 0- Cited by
- 5 results in Mathlib
- Foundations
- Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingDecidableEqFintype
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.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Polynomialproof · cited by 5,681
- Matrixstatement and proof · cited by 4,303
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Fintype.cardstatement and proof · cited by 1,386
- one_smulproof · cited by 1,374
- Polynomial.coeffstatement · cited by 1,045
- neg_negproof · cited by 960
- Polynomial.evalproof · cited by 796
Cited by5
Results whose statement or proof uses this declaration.
- Algebra.PowerBasis.norm_gen_eq_coeff_zero_minpolyproof · cited by 5
- Matrix.det_eq_prod_roots_charpoly_of_splitsproof · cited by 3
- LinearMap.hasEigenvalue_zero_tfaeproof · cited by 2
- Matrix.charpoly_of_card_eq_twoproof · cited by 2
- LinearMap.det_eq_sign_charpoly_coeffproof · cited by 2