Study On Some Inequalities Of Hermite Matrix And Quaternion Matrix

As an important part of mathematical research, Matrix theory and matrix analysishave been widely used in mathematics disciplines and many other scientific fields, suchas computational mathematics, physics, economics, biology, management science andengineering, image analysis etc. As an important content of matrix theory, matrixinequality occupies very important position in matrix theory, and has long beenattracting many scholars’ attention. The purpose of this article is to research the matrixinequalities, in this paper, some of the theory of real number numerical inequality havebeen generalized to the Hermite matrix and quaternion matrix. The main contents are asfollows:1.Studied some inequalities about the trace of Hermite matrix under the Hadamardproduct;2.The classical Wielandt-Hoffman theorem were generalized to the quaternionmatrix, and estimate the upper bound of the theorem;3.Generalized the average inequality, Young, H lder, Minkowski inequality on thequaternion matrix;4.Studied some inequalities of quaternion matrix under the Hadamard product.