GEHD2 - 5.2 English - 68552

    Reduction of a real general matrix a to upper Hessenberg form H by an orthogonal
    similarity transformation:
    Q**T * A * Q = H .

                  The matrix Q is represented as a product of (ihi-ilo) elementary reflectors

                  Q = H(ilo) H(ilo+1) . . . H(ihi-1).

                  Each H(i) has the form

                  H(i) = I - tau * V * V**T

                  where tau is a real scalar, and V is a real vector with V(1:i) = 0, V(i+1) = 1
and V(ihi+1:n) = 0; V(i+2:ihi) is stored on exit in A(i+2:ihi,i), and tau in tau(i).

                  The contents of A are illustrated by the following example, with n = 7, ilo =
2 and ihi = 6: on entry,   on exit,

                  ( a   a   a   a   a   a   a) (  a   a   h   h   h   h   a)
                  (  a   a   a   a   a   a) (   a   h   h   h   h   a)
                  (  a   a   a   a   a   a) (   h   h   h   h   h   h)
                  (  a   a   a   a   a   a) (   v2  h   h   h   h   h)
                  (  a   a   a   a   a   a) (   v2  v3  h   h   h   h)
                  (  a   a   a   a   a   a) (   v2  v3  v4  h   h   h)
                  ( a) (  a)
                  where,
                  a denotes an element of the original matrix a,
                  h denotes a modified element of the upper Hessenberg matrix H,
                  vi denotes an element of the vector defining H(i).