Theorems · Theorem · linear algebra
Matrix.zpow_sub
∀ {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 → ∀ (z1 z2 : ℤ), A ^ (z1 - z2) = A ^ z1 / A ^ z2- Defined in
- Mathlib.LinearAlgebra.Matrix.ZPow
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintypeCommRing
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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
- IsUnitstatement and proof · cited by 1,602
- sub_eq_add_negproof · cited by 1,023
- div_eq_mul_invproof · cited by 715
- Matrix.detstatement and proof · cited by 665
- Matrix.zpow_negproof · cited by 5
- Matrix.zpow_addproof · cited by 3
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