Symbolic Computation of the Duggal Transform

Following the results of , 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 decompositionof a. thereat, the polynomial singular value decomposition method is utilized, which is aniterative algorithm with numerical characteristics. the introduced algorithm is proven andillustrated in numerical examples. we also represent symbolically the duggal transform ofrank-one matrices using cross products of vectors and show that the duggal transform of suchmatrices can be given explicitly by a closed formula and is equal to its aluthge transform.