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On The Eigenvalue Problem For Toeplitz Matrices Generated By Rational Functions, William F. Trench
On The Eigenvalue Problem For Toeplitz Matrices Generated By Rational Functions, William F. Trench
William F. Trench
We give formulas for the characteristic polynomial and eigenvectors of of $n\times n$ Toeplitz matrices generated by a formal Laurent series of a rational function $R(z)$. The formulas are in terms of a certain fixed polynomial with coefficients that are simple functions of $\lambda$ and the coefficients of $R(z)$. The complexity of the formulas is independent of $n$.