Some Matrix Inequalityies and Its Applications

In this paper, we mainly discuss the properties and applications of matrix inequality. Firstly, we establish some important inequalities on characteristic values of quaternion matrices, and extend the inequalities about complex matrices. On the other hand, we get the results on the bounds of the solutions concerned with the coefficient matrices of a special linear system.The main results are:1. getting the Wielandt inequality, Kantorwich inequality, and the trace inequality over the quaternion matrices ,2. getting condition number inequality of partitioned matrices by analyzing self-congruent quaternion matrices,3. building several new inequality on singularities of quaternion matrices, and4. discussing a linear system (?) , giving the control inequalities ofnorms of special partitioned matrices.