Perturbations and Stability
Kevin F. Clancey, Israel Gohberg · Birkhäuser Basel eBooks · 1981
In this chapter we study the influence of perturbations of a matrix function on its factorization and partial indices. It develops that the partial indices are stable only in two special cases. Namely if they are all equal or if the difference between the larger and the smaller is one. We prove this theorem in detail and study how the partial indices vary when the matrix function depends analytically on a parameter or is a rational matrix function of two variables where one of the variables is considered to be a parameter. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.