Localization theorems for eigenvalues of quaternionic matrices

Ostrowski type and Brauer type theorems are derived for the left eigenvalues of quaternionic matrix. We see that the above theorems for the left eigenvalues are also true for the case of right eigenvalues, when the diagonals of quaternionic matrix are real. Some distribution theorems are given in terms of ovals of Cassini that are sharper than the Ostrowski type theorems, respectively, for the left and right eigenvalues of quaternionic matrix. In addition, generalizations of the Gerschgorin type theorems are discussed for both the left and right eigenvalues of quaternionic matrix, and finally, we see that our framework is so developed that generalizes the existing results in the literatures.