Thomas R. Cameron
Department of Mathematics
Washington State University
Title: Constructive Proof of Hessenberg Form
Abstract: Every real and
complex matrix is unitarily similar to matrix in Hessenberg form. This
similarity transformation can be done in a finite number of steps.
Moreover, the QR and QZ algorithms are made cost efficient by a
preliminary reduction to Hessenberg and Hessenberg-Triangular form,
A matrix polynomial, P(z), is a matrix whose entries are scalar
polynomials with real or complex coefficients. In this talk we will
present a construction of Hessenberg form for matrix polynomials. A
preliminary reduction to Hessenberg form has the possibility of making
several algorithms for computing the eigenvalues of a matrix polynomial
We will conclude with possible areas of future research, which include
numerically stable algorithms for computing this Hessenberg form.