Theorems · Theorem · linear algebra
Matrix.transpose_zpow
∀ {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), (A ^ n).transpose = A.transpose ^ n- Defined in
- Mathlib.LinearAlgebra.Matrix.ZPow
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 99 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.
Cites8
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
- Matrix.transposestatement and proof · cited by 389
- zpow_natCastproof · cited by 271
- zpow_negSuccproof · cited by 92
- Matrix.transpose_powproof · cited by 4
- Matrix.transpose_nonsing_invproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.IsSymm.zpowproof · cited by 0