Infinite extensions of Toeplitz matrices (Q2567752)

In the paper under review, the authors derive a formula for the smallest of the ranks of infinite Toeplitz extensions of a finite rectangular Toeplitz matrix. More concretely, they show that if \(T_k\) is a \(k\times (n+1-k)\) Toeplitz matrix and \(\text{rt}\,(T_k)\) denotes the smallest of the ranks of infinite Toeplitz extensions of \(T_k\), then \(\text{rt}\,(T_k)\) is the greatest value of \(k\leq n\) such that either the first row of \(T_k\) cannot be expressed as a linear combination of the subsequent rows, or the last row of \(T_k\) cannot be expressed as a linear combination of the preceding rows.