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- TL;DR Summary
- Modal matrix

**Mentor note: The Tex shown below had to be modified a fair amount to conform to the MathJax on this site.**

Trying to calculate the modal matrix for the following

##A =\begin{pmatrix}

1 && 1/2 && 1/2 \\

0 && 1/2 && -1/2 \\

0 && 1/2 && 1 .5

\end{pmatrix}##

there are two eigenvectors for this matrix

##A =\begin{pmatrix}

1 \\

0 \\

0

\end{pmatrix}##

and

##A =\begin{pmatrix}

0 \\

-1 \\

1

\end{pmatrix}##

using the traditional formula for the generalized eigenvector does not work

##Av2 = \lambda v2 + v1##

and, yet, MATLAB has no problem calculating them as\\

##A =\begin{pmatrix}

1/2 \\

-1/2 \\

1/2

\end{pmatrix}##

##A =\begin{pmatrix}

0 \\

1 \\

0

\end{pmatrix}

##

##A =\begin{pmatrix}

0 \\

-1 \\

1

\end{pmatrix}

##

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