Sum Characterization of Diagonalizable

Corrolary

• Let $T\in \mathcal{L}(V)$
• With $\sigma =\{c_1,\dots ,c_n\}$ as the Eigenvalues of $T$
• With $W_i=ker(T-c_{i}I)$ Then, the following are equivalent:

1. $T$ is Diagonalizable
2. $W_1+\cdots +W_n=V$
3. $W_1\oplus \cdots \oplus W_n=V$