Symbolic computation of the Duggal transform

Subject Areas : Linear and multilinear algebra; matrix theory

D. Pappas ¹ , V. Katsikis ² , I. Stanimirovic ³

1 - Department of Statistics, Athens University of Economics and Business, 76 Patission Str, 10434, Athens, Greece
2 - Department of Economics, Division of Mathematics and Informatics, National and Kapodistrian University of Athens, Athens, Greece
3 - Department of Computer Science, Faculty of Science and Mathematics, University of Nis, Visegradska 33, 18000 Nis, Serbia

Received: 2017-11-09 Accepted : 2018-01-10 Published : 2018-03-01

Keywords: Duggal transform, symbolic computation, polar decomposition, polynomial matrices, rank 1 matrices,

Abstract :

Following the results of \cite{Med}, regarding the Aluthge transform of polynomial matrices, the symboliccomputation 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 matricesusing cross products of vectors and show that the Duggal transform of such matrices can be givenexplicitly by a closed formula and is equal to its Aluthge transform.

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