---
name: "zgeev"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/zgeev.f"
---

# zgeev(3)

Part of [zgeev.f(3)](/zgeev.f/3.md).

## NAME

SRC/zgeev.f

## SYNOPSIS

### Functions/Subroutines

subroutine **zgeev** (jobvl, jobvr, n, a, lda, w, vl, ldvl, vr, ldvr, work, lwork, rwork, info)\
  **ZGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices**

## Function/Subroutine Documentation

### subroutine zgeev (character jobvl, character jobvr, integer n, complex\*16, dimension( lda, \* ) a, integer lda, complex\*16, dimension( \* ) w, complex\*16, dimension( ldvl, \* ) vl, integer ldvl, complex\*16, dimension( ldvr, \* ) vr, integer ldvr, complex\*16, dimension( \* ) work, integer lwork, double precision, dimension( \* ) rwork, integer info)

 **ZGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices**

**Purpose:**

```
!>
!> ZGEEV computes for an N-by-N complex nonsymmetric matrix A, the
!> eigenvalues 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.
!>
```

**Parameters**

*JOBVL*

```
!>          JOBVL is CHARACTER*1
!>          = 'N': left eigenvectors of A are not computed;
!>          = 'V': left eigenvectors of are computed.
!>
```

*JOBVR*

```
!>          JOBVR is CHARACTER*1
!>          = 'N': right eigenvectors of A are not computed;
!>          = 'V': right eigenvectors of A are computed.
!>
```

*N*

```
!>          N is INTEGER
!>          The order of the matrix A. N >= 0.
!>
```

*A*

```
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the N-by-N matrix A.
!>          On exit, A has been overwritten.
!>
```

*LDA*

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

*W*

```
!>          W is COMPLEX*16 array, dimension (N)
!>          W contains the computed eigenvalues.
!>
```

*VL*

```
!>          VL is 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 eigenvalues.
!>          If JOBVL = 'N', VL is not referenced.
!>          u(j) = VL(:,j), the j-th column of VL.
!>
```

*LDVL*

```
!>          LDVL is INTEGER
!>          The leading dimension of the array VL.  LDVL >= 1; if
!>          JOBVL = 'V', LDVL >= N.
!>
```

*VR*

```
!>          VR is 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*

```
!>          LDVR is INTEGER
!>          The leading dimension of the array VR.  LDVR >= 1; if
!>          JOBVR = 'V', LDVR >= N.
!>
```

*WORK*

```
!>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!>
```

*LWORK*

```
!>          LWORK is 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*

```
!>          RWORK is DOUBLE PRECISION array, dimension (2*N)
!>
```

*INFO*

```
!>          INFO is 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 i+1:N of W contain eigenvalues which have
!>                converged.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **178** of file **zgeev.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.