2023/01/30 by Cox, Michael, Meulen, Kevin N. Vander, Van Tuyl, Adam +1
#15A12 #15B99 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2301.13257
The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of a larger class of companion matrices that can be characterized with a Hessenberg form. In this paper, we demonstrate that the Hessenberg form of the Fiedler companion matrices provides a straight-forward way to compare the condition numbers of these matrices. We also show that there are other companion matrices which can provide a much smaller condition number than any Fiedler companion matrix. We finish by exploring the condition number of a class of matrices obtained from perturbing a Frobenius companion matrix while preserving the characteristic polynomial.