Determinantal representations of the quaternion core inverse and its generalizations
The core inverse was introduced in [\textit{O. M. Baksalary} and \textit{G. Trenkler}, Linear Multilinear Algebra 58, No. 5--6, 681--697 (2010; Zbl 1202.15009)]. In this paper, the author investigates the notions of core inverse, core-EP inverse, DMP inverse, and CMP inverse over the quaternion skew-field. Indeed, he studies a direct method to compute their determinantal representations by using column and row noncommutative determinants previously introduced by the author in [Appl. Math. Comput. 219, No. 14, 7632--7644 (2013; Zbl 1291.15040)]. As a special case, the author provides determinantal representations for complex matrices as well. Some useful examples to illustrate the main results are given.
scientific article; zbMATH DE number 7137699
scientific article