Block Toeplitz and Hurwitz Matrices: A Recursive Approach

AbstractRecursive matrices—bi-infinite matrices such that each row can be recursively computed from the previous one—have been revealed to be a useful tool in the study of signal analysis and filter theory. In particular, recursive Toeplitz and Hurwitz matrices are used in [3] to give an algebraic interpretation of signal processing. In this work we introduce the notion of block recursive matrix, and we show that an important property of scalar recursive matrices, namely, the product rule, also holds in the case of block matrices. We also give conditions under which a block Hurwitz matrix of step k can be seen as a scalar Hurwitz matrix of the same step