Solution of Inverse Eigenvalue Problems for Quaternionic Matrices

Abstract

This paper explores inverse eigenvalue problems concerning quaternionic matrices. Initially, we establish a vital criterion determining whether specified sets of complex numbers and quaternionic vectors constitute eigenvalues and their corresponding eigenvectors for certain quaternionic matrices. Subsequently, we provide explicit constructions for the collection of such quaternionic matrices, if they indeed exist. Additionally, within this collection, we identify a specific matrix closest to a given quaternionic matrix. This process involves transforming the problem into a convex optimization challenge. Finally, we verify our findings through various numerical demonstrations.