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When a matrix A is diagonalizable then

[itex]

A= S \Lambda S^{-1}

[/itex]

and the matrix S can be formed from eigenvectors that correspond to the eigenvalues in \Lambda

Question:

how do I form S when A is not diagonalizable?

ie.

[itex]

\left[

\begin{array}{rr}

5&1\\

-1&3\\

\end{array}

\right]

=S \left[

\begin{array}{rr}

4&1\\

0&4\\

\end{array}

\right]

S^{-1}

[/itex]