On Positive Integer Powers of Toeplitz Matrices
Honglin Wu · Journal of Mathematics Research · 2013
In this paper, we restate a necessary and sufficient condition for all positive integer powers of a Toeplitz matrix to be still Toeplitz matrices which was ever studied by T. N. E. Greville (1983) and Tamir Shalom (1987), and our new proof is clear and self-contained. We also derive some identities involving the entries of the Toeplitz matrix and those of its positive integer powers in case that the powers are still Toeplitz matrices.