Theorems · Theorem · linear algebra
Matrix.Commute.zpow_right
∀ {n' : Type u_1} [inst : DecidableEq n'] [inst_1 : Fintype n'] {R : Type u_2} [inst_2 : CommRing R]
{A B : Matrix n' n' R}, Commute A B → ∀ (m : ℤ), Commute A (B ^ m)- Defined in
- Mathlib.LinearAlgebra.Matrix.ZPow
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 115 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.
Cites11
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
- Commutestatement and proof · cited by 639
- zero_powproof · cited by 361
- zpow_natCastproof · cited by 271
- zpow_negSuccproof · cited by 92
- Commute.pow_rightproof · cited by 12
- Matrix.isUnit_det_of_left_inverseproof · cited by 5
- Matrix.nonsing_inv_cancel_or_zeroproof · cited by 4
- Matrix.SemiconjBy.zpow_rightproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Matrix.Commute.zpow_leftproof · cited by 2
- Matrix.Commute.zpow_zpowproof · cited by 1
- Matrix.Commute.self_zpowproof · cited by 0