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A matrix of the form
References
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T.  ``Reduction of a General Matrix to
  Hessenberg Form.''  §11.5 in
  Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed.  Cambridge, England:
  Cambridge University Press, pp. 476-480, 1992.