Eigenvectors of Real and Complex Matrices by LR and QR triangularizations

  • G. Peters
  • J. H. Wilkinson
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 186)


In a recent paper [4] the triangularization of complex Hessenberg matrices using the LR algorithm was described. Denoting the Hessenberg matrix by H and the final triangular matrix by T we have
$$ {P^{ - 1}}HP = T, $$
where P is the product of all the transformation matrices used in the execution of the LR algorithm. In practice H will almost invariably have been derived from a general complex matrix A using the procedure comhes [3] and hence for some nonsingular S we have
$$ {P^{ - 1}}{S^{ - 1}}ASP = T. $$


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© Springer-Verlag Berlin · Heidelberg 1971

Authors and Affiliations

  • G. Peters
  • J. H. Wilkinson

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