The resultant matrix of two polynomials

A companion matrix resultant for Bernstein polynomials

On the distance from a matrix polynomial to matrix polynomials with two prescribed eigenvalues

Consider an n × <span style="fon...

Resultant and Discriminant of Polynomials

This is a collection of classical results about resultants and discriminants for polynomials, compiled mainly for my own use. All results are well-known 19th century mathematics, but I have not investigated the history, and no references are given. 1. Resultant Definition 1.1. Let f(x) = anx n + · · ·+ a0 and g(x) = bmx + · · ·+ b0 be two polynomials of degrees (at most) n and m, respectively, ...

On the resultant of degree-deficient polynomials

The resultant is an algebraic expression, computable in a finite number of arithmetic operations from the coefficients of two univariate polynomials, that vanishes if, and only if, the two polynomials have common zeros. The paper considers formal resultant for degree-deficient polynomials (polynomials whose actual degree is lower than their assumed degree). Some key properties of the resultant ...

Some Results on the Field of Values of Matrix Polynomials

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 ...