Numerical procedures are proposed for triangularizing polynomial matrices over the eld of polynomial fractions and over the ring of polynomials. They are based on two standard polynomial techniques: Sylvester matrices and interpolation. In contrast to other triangularization methods, the algorithms described in this paper only rely on well-worked numerically reliable tools. They can also be use...

Some properties of near-Toeplitz tridiagonal matrices with specific perturbations in the first and last main diagonal entries are considered. Applying the relation between the determinant and Chebyshev polynomial of the second kind, we first give the explicit expressions of determinant and characteristic polynomial, then eigenvalues are shown by finding the roots of the characteristic polynomia...

Some properties of near-Toeplitz tridiagonal matrices with specific perturbations in the first and last main diagonal entries are considered. Applying the relation between the determinant and Chebyshev polynomial of the second kind, we first give the explicit expressions of determinant and characteristic polynomial, then eigenvalues are shown by finding the roots of the characteristic polynomia...

In this paper, the notions of pseudofield of values and joint pseudofield of values of matrix polynomials are introduced and some of their algebraic and geometrical properties are studied.  Moreover, the relationship between the pseudofield of values of a matrix polynomial and the pseudofield of values of its companion linearization is stated, and then some properties of the augmented field of ...

New Schur stability checking method of the polynomial matrices whose coefficient matrix are interval matrices is presented in this paper. In the suggested method, the interval Markov matrices of the interval polynomial matrix are used to assess its stability. The validity of the suggested methods is illustrated through numerical examples. The main contribution of the suggested method is that it...

Amitsur's formula, which expresses det(A + B) as a polynomial in coefficients of the characteristic polynomial of a matrix, is generalized for partial linearizations of the pfaffian of block matrices. As applications, in upcoming papers we determine generators for the SO(n)-invariants of several matrices and relations for the O(n)-invariants of several matrices over a field of arbitrary charact...

Let P and Q be nr, r n matrices with Laurent polynomial entries. Suppose that Q T (z)P (z) = I r , z 2 Cnf0g. This note provides an algorithmatic construction of two n(nr) matrices G and H with Laurent polynomial entries such that the nn matrices