Theorems · Definition · linear algebra
Matrix.detMonoidHom
{n : Type u_2} →
[inst : DecidableEq n] → [inst_1 : Fintype n] → {R : Type v} → [inst_2 : CommRing R] → Matrix n n R →* RThe determinant of a matrix, as a monoid homomorphism.
- Cited by
- 6 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 · cited by 4,303
- MonoidHomstatement · cited by 3,629
- Matrix.detproof · cited by 665
- Matrix.det_mulproof · cited by 51
- Matrix.det_oneproof · cited by 35
Cited by7
Results whose statement or proof uses this declaration.
- Matrix.det_powproof · cited by 7
- Matrix.specialUnitaryGroupproof · cited by 4
- Matrix.isUnit_charpolyRev_of_isNilpotentproof · cited by 2
- FiniteField.Matrix.charpoly_pow_cardproof · cited by 2
- Matrix.coe_detMonoidHomstatement · cited by 1
- LinearMap.detAux_defstatement and proof · cited by 1
- LinearMap.detAux_def'proof · cited by 1