Originally Posted by

**superdude** How do you know which eigenvectors are which column? Does it matter? So in my example if I found the eigenvectors how would I know it wouldn't be $\displaystyle

D=\left[ {\begin{array}{cc}

0 & 2 \\

-3 & 0 \\

\end{array} } \right]

$

This matrix isn't diagonal so it cannot be in our case , and if the first eigenvalue appears in D then the first column of the invertible matrix P will be an eigenvector corresponding to this eigenvalue...

Tonio

Is it because we start with the smallest values of $\displaystyle \lambda$ and work our way up and the eigenvectors found get put into the matrix D left from right? If this is true, then what happens if 2 eigenvectors are associated with one eigenvalue (is this even possible)?