Theorems · Theorem · linear algebra
Matrix.zpow_neg
∀ {n' : Type u_1} [inst : DecidableEq n'] [inst_1 : Fintype n'] {R : Type u_2} [inst_2 : CommRing R]
{A : Matrix n' n' R}, IsUnit A.det → ∀ (n : ℤ), A ^ (-n) = (A ^ n)⁻¹- Defined in
- Mathlib.LinearAlgebra.Matrix.ZPow
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 108 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
- IsUnitstatement and proof · cited by 1,602
- Matrix.detstatement and proof · cited by 665
- zpow_natCastproof · cited by 271
- zpow_negSuccproof · cited by 92
- IsUnit.powproof · cited by 48
- Matrix.det_powproof · cited by 7
- Matrix.zpow_neg_natCastproof · cited by 6
- Matrix.nonsing_inv_nonsing_invproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Matrix.zpow_add_oneproof · cited by 3
- Matrix.zpow_subproof · cited by 0
- Matrix.exp_zsmulproof · cited by 0
- Matrix.inv_zpow'proof · cited by 0
- Matrix.zpow_neg_mul_zpow_selfproof · cited by 0