Theorems · Theorem · linear algebra
Matrix.zpow_neg_natCast
∀ {n' : Type u_1} [inst : DecidableEq n'] [inst_1 : Fintype n'] {R : Type u_2} [inst_2 : CommRing R]
(A : Matrix n' n' R) (n : ℕ), A ^ (-↑n) = (A ^ n)⁻¹- Defined in
- Mathlib.LinearAlgebra.Matrix.ZPow
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 106 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.
Cites9
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
- pow_zeroproof · cited by 1,094
- neg_zeroproof · cited by 542
- CharP.cast_eq_zeroproof · cited by 357
- inv_oneproof · cited by 301
- zpow_ofNatproof · cited by 144
- DivInvMonoid.zpow_neg'proof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- Matrix.zpow_negproof · cited by 5
- Matrix.zpow_mulproof · cited by 1
- Matrix.isUnit_det_zpow_iffproof · cited by 0
- Matrix.zpow_add_of_nonposproof · cited by 0
- Matrix.PosSemidef.zpowproof · cited by 0
- Matrix.zpow_add_one_of_ne_neg_oneproof · cited by 0