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 charac...

Matrix functions are used in many areas of linear algebra and arise in numerical applications in science and engineering. In this paper, we introduce an effective approach for determining matrix function f(A)=g(q(A)) of a square matrix A, where q is a polynomial function from a degree of m and also function g can be a transcendental function. Computing a matrix function f(A) will be time- consu...

Landry, Minsky and Taylor defined the taut polynomial of a veering triangulation. Its specialisations generalise Teichmuller fibred face Thurston norm ball. We prove that triangulation is equal to certain twisted Alexander underlying manifold. Then we give formulas relating untwisted polynomial. There are two formulas; one holds when maximal free abelian cover edge-orientable, another it not ed...