Theorems · Theorem · linear algebra
Matrix.det_neg
∀ {n : Type u_2} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] (A : Matrix n n R),
(-A).det = (-1) ^ Fintype.card n * A.det- Cited by
- 14 results in Mathlib
- Foundations
- Depth 91 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Fintype.cardstatement · cited by 1,386
- Matrix.detstatement and proof · cited by 665
- neg_one_smulproof · cited by 23
- Matrix.det_smulproof · cited by 11
Cited by14
Results whose statement or proof uses this declaration.
- Matrix.isElliptic_neg_iffproof · cited by 3
- Matrix.IsParabolic.negproof · cited by 2
- Matrix.isHyperbolic_neg_iffproof · cited by 2
- Matrix.charpoly_mul_comm'proof · cited by 2
- UpperHalfPlane.gl_smul_eq_self_iff_eq_fixedPtproof · cited by 1
- Ideal.FinrankQuotientMap.span_eq_topproof · cited by 1
- Submodule.det_reflectionproof · cited by 1
- MvPolynomial.universalFactorizationMapPresentation_jacobianproof · cited by 1
- UpperHalfPlane.fixedPt_negproof · cited by 1
- UpperHalfPlane.σ_negproof · cited by 1
- Matrix.charpoly_coeff_eq_sum_minorsproof · cited by 0
- Matrix.charpoly_invproof · cited by 0