Theorems · Theorem · linear algebra
Matrix.det_pow
∀ {m : Type u_1} [inst : DecidableEq m] [inst_1 : Fintype m] {R : Type v} [inst_2 : CommRing R] (M : Matrix m m R)
(n : ℕ), (M ^ n).det = M.det ^ n- Cited by
- 7 results in Mathlib
- Foundations
- Depth 92 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.
Cites6
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
- Matrix.detstatement · cited by 665
- MonoidHom.map_powproof · cited by 30
- Matrix.detMonoidHomproof · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- Matrix.zpow_negproof · cited by 5
- IsUnit.det_zpowproof · cited by 2
- Matrix.SemiconjBy.zpow_rightproof · cited by 1
- Algebra.Norm.Transitivity.det_det_auxproof · cited by 1
- Matrix.zpow_mulproof · cited by 1
- Matrix.pow_sub'proof · cited by 0
- Matrix.isUnit_det_zpow_iffproof · cited by 0