Abstract
SummaryIn this article, we extend the results for Toeplitz matrices obtained by Noschese, Pasquini, and Reichel. We study the distance d, measured in the Frobenius norm, of a real tridiagonal 2‐Toeplitz matrix T to the closure of the set formed by the real irreducible tridiagonal normal matrices. The matrices in , whose distance to T is d, are characterized, and the location of their eigenvalues is shown to be in a region determined by the field of values of the operator associated with T, when T is in a certain class of matrices that contains the Toeplitz matrices. When T has an odd dimension, the eigenvalues of the closest matrices to T in are explicitly described. Finally, a measure of nonnormality of T is studied for a certain class of matrices T. The theoretical results are illustrated with examples. In addition, known results in the literature for the case in which T is a Toeplitz matrix are recovered.
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