# Ubuntu Feisty 7.04 manual page repository

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### NAME

```        ZGEEV - compute for an N-by-N complex nonsymmetric matrix A, the eigen‐
values and, optionally, the left and/or right eigenvectors
```

### SYNOPSIS

```        SUBROUTINE ZGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR, WORK,
LWORK, RWORK, INFO )

CHARACTER     JOBVL, JOBVR

INTEGER       INFO, LDA, LDVL, LDVR, LWORK, N

DOUBLE        PRECISION RWORK( * )

COMPLEX*16    A(  LDA,  *  ), VL( LDVL, * ), VR( LDVR, * ), W( * ),
WORK( * )
```

### PURPOSE

```        ZGEEV computes for an N-by-N complex nonsymmetric matrix A, the  eigen‐
values  and, optionally, the left and/or right eigenvectors.  The right
eigenvector v(j) of A satisfies
A * v(j) = lambda(j) * v(j)
where lambda(j) is its eigenvalue.
The left eigenvector u(j) of A satisfies
u(j)**H * A = lambda(j) * u(j)**H
where u(j)**H denotes the conjugate transpose of u(j).

The computed eigenvectors are normalized to have Euclidean  norm  equal
to 1 and largest component real.
```

### ARGUMENTS

```        JOBVL   (input) CHARACTER*1
= ’N’: left eigenvectors of A are not computed;
= ’V’: left eigenvectors of are computed.

JOBVR   (input) CHARACTER*1
= ’N’: right eigenvectors of A are not computed;
= ’V’: right eigenvectors of A are computed.

N       (input) INTEGER
The order of the matrix A. N >= 0.

A       (input/output) COMPLEX*16 array, dimension (LDA,N)
On  entry,  the N-by-N matrix A.  On exit, A has been overwrit‐
ten.

LDA     (input) INTEGER
The leading dimension of the array A.  LDA >= max(1,N).

W       (output) COMPLEX*16 array, dimension (N)
W contains the computed eigenvalues.

VL      (output) COMPLEX*16 array, dimension (LDVL,N)
If JOBVL = ’V’, the left eigenvectors u(j) are stored one after
another in the columns of VL, in the same order as their eigen‐
values.  If JOBVL = ’N’, VL is not referenced.  u(j) = VL(:,j),
the j-th column of VL.

LDVL    (input) INTEGER
The  leading  dimension of the array VL.  LDVL >= 1; if JOBVL =
’V’, LDVL >= N.

VR      (output) COMPLEX*16 array, dimension (LDVR,N)
If JOBVR = ’V’, the right  eigenvectors  v(j)  are  stored  one
after  another in the columns of VR, in the same order as their
eigenvalues.  If JOBVR = ’N’, VR is  not  referenced.   v(j)  =
VR(:,j), the j-th column of VR.

LDVR    (input) INTEGER
The  leading  dimension of the array VR.  LDVR >= 1; if JOBVR =
’V’, LDVR >= N.

WORK    (workspace/output) COMPLEX*16 array, dimension (LWORK)
WORK(1) returns the optimal LWORK.

LWORK   (input) INTEGER
The dimension of the array WORK.   LWORK  >=  max(1,2*N).   For
good performance, LWORK must generally be larger.

If  LWORK  = -1, then a workspace query is assumed; the routine
only calculates the optimal size of  the  WORK  array,  returns
this  value  as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.

RWORK   (workspace) DOUBLE PRECISION array, dimension (2*N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value.
> 0:  if INFO = i, the QR algorithm failed to compute  all  the
eigenvalues,  and  no eigenvectors have been computed; elements
and i+1:N of W contain eigenvalues which have converged.

```
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