Cyclic Subspaces

The smallest subspace comprised of compositions of transform on the same vector.

Definition

1. For a non-zero Vector $v$
2. For the smallest $k$ that allows for $\{v,T(v),T^2(v),\dots ,T^k(v)\}$
3. The cyclic subspace is $C_v=\{v,T(v),T^{k-1}(v)\}$

Theorems

• Cyclic Decomposition Theorem