Theorems · Theorem · linear algebra
Matrix.zpow_add_one_of_ne_neg_one
∀ {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 : ℤ), n ≠ -1 → A ^ (n + 1) = A ^ n * A- Defined in
- Mathlib.LinearAlgebra.Matrix.ZPow
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintypeCommRing
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Cites12
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
- MulZeroClass.zero_mulproof · cited by 1,625
- MonoidWithZeroproof · cited by 456
- pow_succproof · cited by 374
- zero_powproof · cited by 361
- zpow_natCastproof · cited by 271
- Matrix.zpow_neg_natCastproof · cited by 6
- Matrix.isUnit_det_of_left_inverseproof · cited by 5
- Matrix.nonsing_inv_cancel_or_zeroproof · cited by 4
- Matrix.zpow_add_oneproof · cited by 3
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