Outer inverse of reduced biquaternion matrices

Abstract

This article focuses on computing the outer and {1,2}-generalized inverse of reduced biquaternion matrices (RBGI). The main results refer to RBGI that fulfill predefined conditions on column and/or row space. Conditions for the existence and effective representations of these generalized inverses are introduced. The existence condition is determined using the rank function and regularity, while representation is achieved by solving reduced biquaternion (RB) matrix equations. Additionally, numerical algorithms arising from these representations are presented, and their effectiveness is demonstrated through numerical examples. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.