Solving Systems of Linear Equations with Normal Coefficient Matrices and the Degree of the Minimal Polyanalytic Polynomial

The generalized Lanczos process applied to a normal matrix $A$ builds up a condensed form of $A$, which can be described as a band matrix with slowly growing bandwidth. For certain classes of normal matrices, the bandwidth turns out to be constant. It is shown that, in such cases, the bandwidth is determined by the degree of the minimal polyanalytic polynomial of $A$. It was in relation to the generalized Lanczos process that M. Huhtanen introduced the concept of the minimal polyanalytic polynomial of a normal matrix.