Nearness results for real tridiagonal 2‐Toeplitz matrices

Summary In 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 closureN T Rof the set formed by the real irreducible tridiagonal normal matrices. The matrices inN T R , 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 inN T Rare 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.