The Quaternion Matrix Eigenvalue

In this paper, we are devoted to investigating the left and right eigenvalues of quaternionic matrices, as well as the corresponding characteristic equations on left and right eigenvalues. And we will generalize some well-known results on Gersogorin theorem.In Chapter 1, we will show some preliminary knowledge so as to help comprehend the whole paper.In Chapter 2, we will sum up some properties on the right eigenvalues, and investigate the right characteristic equations of 2-order and 3-order quaternionic matrices.In Chapter 3, we will investigate the left eigenvalues and the left characteristic equations of 2-order and 3-order quaternionic matrices.In Chapter 4, we will mainly generalize Gersogorin theorem and estimate the left and right eigenvalues of a quaternionic matrix.In the last chapter, we will propose some conjectures and some unresolved problems.