Example 2 (from Program LA_GGEV_EXAMPLE)

$$A = \left( \begin{array}{rrrrr} -2 + 2i & -9 + 3i & 1 ... ...-8 + i & 5 + -i & 10 -4i & -4 + 0i \end{array} \right)$$

$$B = \left( \begin{array}{rrrrr} -7 + 0i & 5 + i & 4 + ... ...-1 + 4i & -2 + 3i & -2 -3i & -10 -i \end{array} \right)$$

Arrays ${\bf A}$and B on entry:

$$\begin{array}{c} {\bf A} \\ \begin{array}{\vert rrrrr\ver... ... -1) & (10, -4)& (-4, 0) \\ \hline \end{array} \end{array}$$

$$\begin{array}{c} {\bf B} \\ \begin{array}{\vert rrrrr\ver... ...3) & (-2, -3) & (-10, -1) \\ \hline \end{array} \end{array}$$

The call:
CALL LA_GGEV( A, B, ALPHA, BETA, VL, VR, INFO )

ALPHA, BETA, INFO, VL and VR on exit:

$$\begin{array}{cc} {\bf ALPHA} \\ \begin{array}{\vert ll\v... ...y} \hspace{0.50 cm} \begin{array}{c} {\bf INFO} = 0 \end{array}$$

$$\begin{array}{c} {\bf VL} \\ \begin{array}{\vert ll} \hline... ...},~~4.06072 \times 10^{-1}) \\ \hline \end{array} \end{array}$$

$$\begin{array}{lll\vert} \hline (~~0,0) & (~~0,0) & (0,0) \\ ... ...0^{-1},4.77557 \times 10^{-1}) & (1, 0)\\ \hline \end{array}$$

$$\begin{array}{c} {\bf VR} \\ \begin{array}{\vert lll} \hlin... ... (~~0.00000~~~~~,~~0.00000) \\ \hline \end{array} \end{array}$$

$$\begin{array}{ll\vert} \hline (9.97417 \times 10^{-2},-3.22... ...0) & (~~7.50905 \times 10^{-1},0.00000) \\ \hline \end{array}$$

The eigenvalues of the problem $A z = \lambda B z$ are:

$$\left( \begin{array}{ll} -2.56692~~~~ & + 4.01547 \times 10^... ...times 10^{-2} & + 1.18506 \times 10^{-1}i \end{array} \right).$$

The left generalized eigenvectors are:

$$\left( \begin{array}{ll} ~~8.44783 \times 10^{-1} & ~~0 \\ ~... ...5 \times 10^{-2}+4.06072 \times 10^{-1}i \end{array} \right.$$

$$\left. \begin{array}{lll} ~~0 & ~~0 & 0 \\ ~~0 & ~~0 & ... ...{-1} + 4.77557 \times 10^{-1}i & 1.00000 \end{array} \right),$$

The right generalized eigenvectors are:

$$\left( \begin{array}{lll} 1.00000+0.00000i & 5.94957 \times... ...0000 \\ 0.00000 & 0.00000 & ~~0.00000 \end{array} \right.$$

$$\left. \begin{array}{ll} 9.97417 \times 10^{-2}-3.22876 \tim... ...\\ 0.00000 & ~~7.50905 \times 10^{-1} \end{array} \right).$$