Example 2 (from Program LA_GEEV_EXAMPLE)

$$A = \left( \begin{array}{ccccc} -6 & 5 & 8 + i & -1 ... ... & 2 -2i & 2i & -2 + 4i & -6 -2i \end{array} \right)$$

$$\begin{array}{c} {\bf A} \\ \begin{array}{\vert rrrrr\ver... ...) & ( -2 , 4) & ( -6 , -2) \\ \hline \end{array} \end{array}$$

The call:
CALL LA_GEEV( A, W, VL, VR, INFO )

${\bf W}$, ${\bf VL}$, ${\bf VR}$, and ${\bf INFO}$ on exit:

$$\begin{array}{cc} {\bf W} \\ \begin{array}{\vert l\vert} ... ...\;\;\; 2.41177) \\ \hline \end{array} \end{array}\hspace{5mm}$$

$$\begin{array}{c} {\bf VL} \\ \begin{array}{\vert ll} \hlin... ...es 10^{-1}, \;\;\; 0.00000 ) \\ \hline \end{array}\end{array}$$

$$\begin{array}{c} {\bf VL}\ (continued) \\ \begin{array}{ll... ...\;\; 3.10209 \times 10^{-1}) \\ \hline \end{array}\end{array}$$

$$\begin{array}{c}{\bf VL}\ (continued) \\ \begin{array}{l\v... ...es 10^{-1}, \;\;\; 0.00000) \\ \hline \end{array} \end{array}$$

$$\begin{array}{c}{\bf VR} \\ \begin{array}{\vert ll} \hline... ...es 10^{-1}, \;\;\; 0.00000) \\ \hline \end{array} \end{array}$$

$$\begin{array}{c}{\bf VR}\ (continued) \\ \begin{array}{ll}... ...;\; 1.07102 \times 10^{-1}) \\ \hline \end{array} \end{array}$$

$$\begin{array}{c}{\bf VR}\ (continued) \\ \begin{array}{l\v... ...y} \hspace{1.00 cm} \begin{array}{c} {\bf INFO} = 0 \end{array}$$

The eigenvalues of matrix $A$ are:

$$\left( \begin{array}{r} -11.3885 \;\;\;\;\;\;\; -4.99204i \... ...9i \\ -9.75794 \times 10^{-1} +2.41177i \end{array} \right).$$

The left and right eigenvectors of matrix $A$ are (columnwise):

$$\left( \begin{array}{ll} -4.42699 \times 10^{-1} - 1.09152 \... ...}i & \;\;\; 5.738012 \times 10^{-1} \\ \end{array} \right.$$

$$\left. \begin{array}{ll} -2.41800 \times 10^{-1} + 1.14309 \... ...\times 10^{-1} + 3.10209 \times 10^{-1}i \end{array} \right.$$

$$\left. \begin{array}{l} \;\;\; 2.32683 \times 10^{-1} + 4.... ...2}i \\ \;\;\; 6.43074 \times 10^{-1} \\ \end{array} \right)$$

and

$$\left( \begin{array}{ll} \;\;\; 6.16325 \times 10^{-1} & -... ...1}i & \;\;\; 6.72618 \times 10^{-1} \\ \end{array} \right.$$

$$\left. \begin{array}{ll} \;\;\; 1.74764 \times 10^{-1} - 8.... ...es 10^{-1} + 1.07102 \times 10^{-1}i \\ \end{array} \right.$$

$$\left. \begin{array}{l} \;\;\; 7.45969 \times 10^{-1} \\ \;... ...s 10^{-1} + 1.63665 \times 10^{-1}i \\ \end{array} \right).$$