Symbolic computation of the Duggal transform

Authors

  • D. Pappas Department of Statistics, Athens University of Economics and Business, 76 Patission Str, 10434, Athens, Greece
  • I. Stanimirovic Department of Computer Science, Faculty of Science and Mathematics, University of Nis, Visegradska 33, 18000 Nis, Serbia
  • V. Katsikis Department of Economics, Division of Mathematics and Informatics, National and Kapodistrian University of Athens, Athens, Greece
Abstract:

Following the results of cite{Med}, regarding the Aluthge transform of polynomial matrices, the symbolic computation of the Duggal transform of a polynomial matrix $A$ is developed in this paper, using the polar decomposition and the singular value decomposition of $A$. Thereat, the polynomial singular value decomposition method is utilized, which is an iterative algorithm with numerical characteristics. The introduced algorithm is proven and illustrated in numerical examples. We also represent symbolically the Duggal transform of rank-one matrices using cross products of vectors and show that the Duggal transform of such matrices can be given explicitly by a closed formula and is equal to its Aluthge transform.

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Journal title

volume 07  issue 01

pages  53- 62

publication date 2018-03-01

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