## Householder's Method for Complex Matrices and Eigensystems of Hermitian Matrices |

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Algol procedure householder Algol variable ALPHA(J Argonne National Laboratory arithmetic code back transformation begin real calculates the eigensystem calling program CCNJ CDC 3600 computer column vector complex arithmetic COMPLEX CONJUGATE complex matrix complex vector tau contains the diagonal delta diagonal unitary similarity double precision eigenvalues and eigenvectors Euclidean norm EXPONENT FAULT hermitian matrix Hessenberg form Householder matrices Householder reduction HOUSEHOLDER TRANSFORMATION integer j.rml lower subdiagonal lower triangle matrix of order matrix z1 millisec MSUB multiple eigenvalue NMAX NSUB original matrix output procedure householder hermitian procedure householder nonhermitian procedure tridibisectionl procedure tridiinverse iteration ratio real arithmetic real array real matrix REAL PART IMAGINARY real symmetric matrix real symmetric tridiagonal real vector reduced matrix rhol routine scalar step subroutine eigen symmetric matrix symmetric tridiagonal matrix TAU(I TAUl TEMP temporarily stored transforms the eigenvectors tridiagonal real TYPE COMPLEX unitary matrix upper Hessenberg matrix upper triangle VTEMP zero zero matrix