Shell extremal eigenvalues of tridiagonal Toeplitz Matrices

Abstract

The shell of a complex tridiagonal Toeplitz matrix is studied. Closed formulas for all quantities involved in its equation are presented. Necessary and sufficient conditions for a Toeplitz tridiagonal matrix to have shell extremal eigenvalues are given. Several, recently introduced, geometric quantities related to the shell are studied as measures of non-normality of these extremal eigenvalues of such matrices. These quantities are also proposed as measures of non-normality for the matrix itself.