A Family of Maximal Algebras of Block Toeplitz matrices

TL;DR

This paper explores specific families of maximal commutative algebras within block Toeplitz matrices, extending the understanding of their algebraic structure beyond classical circulants.

Contribution

It introduces and studies new families of maximal commutative algebras for block Toeplitz matrices, which lack simple descriptions like those for scalar Toeplitz matrices.

Findings

Identified new families of maximal commutative algebras for block Toeplitz matrices.

Extended the algebraic classification beyond classical circulant cases.

Provided structural insights into block Toeplitz algebraic properties.

Abstract

The maximal commutative subalgebras containing only Toeplitz matrices have been identified as generalized circulants. A similar simple description cannot be obtained for block Toeplitz matrices. We introduce and investigate certain families of maximal commutative algebras of block Toeplitz matrices.