This paper presents a framework for computing the structure-constrained least
squares solutions to the generalized reduced biquaternion matrix equations
(RBMEs). The investigation focuses on three different matrix equations: a
linear matrix equation with multiple unknown L-structures, a linear matrix
equation with one unknown L-structure, and the general coupled linear matrix
equations with one unknown L-structure. Our approach leverages the complex
representation of reduced biquaternion matrices. To showcase the versatility of
the developed framework, we utilize it to find structure-constrained solutions
for complex and real matrix equations, broadening its applicability to various
inverse problems. Specifically, we explore its utility in addressing partially
described inverse eigenvalue problems (PDIEPs) and generalized PDIEPs. Our
study concludes with numerical examples.Comment: 30 page