On certain matrices related to the Cauchy and Toeplitz matrices

Abstract

In this paper, we introduce a new class of matrices with no singular sub-matrices over a field of arbitrary characteristics. To do this end, we first compute the determinant of a certain type of square matrices, which are related to the well-known Cauchy, Toeplitz, and Hilbert matrices in a special case. It is also shown that all of the minors of those matrices have full rank. Then, applying our results, we determine the rank of a newly introduced class of matrices under study.