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### NAME

ZGEBAK - form the right or left eigenvectors of a complex general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by ZGEBAL

### SYNOPSIS

SUBROUTINE ZGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV, INFO ) CHARACTER JOB, SIDE INTEGER IHI, ILO, INFO, LDV, M, N DOUBLE PRECISION SCALE( * ) COMPLEX*16 V( LDV, * )

### PURPOSE

ZGEBAK forms the right or left eigenvectors of a complex general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by ZGEBAL.

### ARGUMENTS

JOB (input) CHARACTER*1 Specifies the type of backward transformation required: = ’N’, do nothing, return immediately; = ’P’, do backward transforma‐ tion for permutation only; = ’S’, do backward transformation for scaling only; = ’B’, do backward transformations for both permutation and scaling. JOB must be the same as the argument JOB supplied to ZGEBAL. SIDE (input) CHARACTER*1 = ’R’: V contains right eigenvectors; = ’L’: V contains left eigenvectors. N (input) INTEGER The number of rows of the matrix V. N >= 0. ILO (input) INTEGER IHI (input) INTEGER The integers ILO and IHI determined by ZGEBAL. 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. SCALE (input) DOUBLE PRECISION array, dimension (N) Details of the permutation and scaling factors, as returned by ZGEBAL. M (input) INTEGER The number of columns of the matrix V. M >= 0. V (input/output) COMPLEX*16 array, dimension (LDV,M) On entry, the matrix of right or left eigenvectors to be trans‐ formed, as returned by ZHSEIN or ZTREVC. On exit, V is over‐ written by the transformed eigenvectors. LDV (input) INTEGER The leading dimension of the array V. LDV >= max(1,N). INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value.