On Some Algebraic Properties of Block Toeplitz Matrices with Commuting Entries

Toeplitz matrices are ubiquitous and play important roles across many areas of mathematics. In this paper, we present some algebraic results concerning block Toeplitz matrices with block entries belonging to a commutative algebra $\mathring{A}$. The characterization of normal block Toeplitz matrices with entries from $\mathring{A}$ is also obtained.