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Symbolic Computation of the Aluthge Transform

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Abstract

The algorithm for the symbolic computation of the Aluthge transform of a polynomial matrix is derived in this paper. For this purpose, the well-known PSVD by PQRD algorithm is considered to avoid square roots of polynomials in the Aluthge transform matrix. The algorithm for the symbolic computation of the polar decomposition for polynomial matrices is developed as well. Furthermore, the Aluthge transform for rank-one matrices defined by cross-products of vectors is symbolically calculated and presented in a closed formula.

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Authors and Affiliations

  1. Department of Statistics, Athens University of Economics and Business, 76 Patission Str, 10434, Athens, Greece

    Dimitrios Pappas

  2. Division of Mathematics and Informatics, Department of Economics, National and Kapodistrian University of Athens, Athens, Greece

    V. N. Katsikis

  3. Department of Computer Science, Faculty of Science and Mathematics, University of Niš, Višegradska 33, 18000, Niš, Serbia

    Ivan P. Stanimirović

Authors
  1. Dimitrios Pappas
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  2. V. N. Katsikis
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  3. Ivan P. Stanimirović
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Correspondence to Dimitrios Pappas.

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Pappas, D., Katsikis, V.N. & Stanimirović, I.P. Symbolic Computation of the Aluthge Transform. Mediterr. J. Math. 14, 45 (2017). https://doi.org/10.1007/s00009-017-0862-5

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  • DOI: https://doi.org/10.1007/s00009-017-0862-5

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