Suppose that $A$ is a diagonalizable matrix with real entries. Show that there is a matrix $C$ with real entries such that $C^3 = A$.
2026-03-25 14:26:07.1774448767
Prove the existence of a matrix $C$ s.t. $C^3=A$
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Put $A=PDP^{-1}$ where $D$ is diagonal.
You can find $E$ such that $D= E^3$.
Finally, write $C=PEP^{-1}$.