Explicit Inverses of Some Special Matrices and Their Applications

Abstract

Matrices, as powerful mathematical constructs, find extensive utility in diverse real-world applications, ranging from engineering and physics to computer science and economics. In recent years, the topic of matrix inverses has started to attract the attention of  many researchers. In this study, we investigate the inverse of some triangular polynomial matrices, which are  formed by conditional polynomial sequences, with the help of some analytical techniques. We derive some correlations between conditional polynomial matrices and the T-nomial matrices of the first and of the second kind. In addition, we get factorizations of the conditional polynomial matrices via T-nomial matrices. Moreover, we obtain several combinatorial identities and provide more generalized results. Finally, we provide some numerical results which explain our method is faster and efficient than MATHEMATICA's Inverse method while computing the inverses of non-singular conditional polynomial matrices.