Nonsingularity of some combinations of tripotent matrices and group invertible matrices

Keywords: Nonsingularity; Idempotent matrix; Tripotent matrix; Group invertible matrix; Diagonalization.This study consists of three main parts. In the Chapter 1, about the application areas of the concepts discussed in this study, information are given.In the Chapter 2, being base for the other chapters, some concepts, properties, and theorems are given.In the Chapter 3, some basic informations and theorems are given about group invertible matrices and tripotent matrices, which are necessary for the Chapter 4.In the Chapter 4, it is established necessary and sufficient conditions for the nonsingularity of combinations where are tripotent matrices and are complex numbers. Moreover, it is obtained some results for the inverse of such combinations. Some of these results are given in terms of group invertible matrices.