On the solutions and perturbation analysis of generalized reduced Biquaternion matrix equations with applications

Abstract

This thesis establishes comprehensive frameworks for addressing generalized reduced biquaternion matrix equations (RBMEs), exploring their solutions, applications, and sensitivity to perturbations. Firstly, the thesis focuses on structured least squares solutions for generalized RBMEs. To this end, it introduces the concept of reduced biquaternion L-structures, which accommodate linear relationships between matrix entries. A comprehensive framework is established for deriving L-structure least squares solutions to RBMEs, with particular attention to specialized structures such as Toeplitz, Hankel, symmetric Toeplitz, and circulant matrices. The developed techniques are further extended to applications like color image restoration and solving partially described inverse eigenvalue problems (PDIEPs) and generalized PDIEPs.