Say $X \in \mathbb{R}^{n\times n}$ is diagonalizable, then one can find the eigenvalue decomposition: $$ X = T \Lambda T^{-1},$$ where each column of $T$ can be viewed as normalized eigenvectors of $X$.
Question
Is there any property on $T$? Say singular value of $T$? I know if $X$ is symmetric, then we have everything desired... But in general, since $T$ is normalized, is there any nice property?