Study On The Numerical Characteristics Of Complex Matrices And Some Inequalities Of Hermite Matrix

As an important tool to study mathematics, matrix has been widely used inmathematical physics, computational mathematics, biology, control theory, imageprocessing and other fields. This paper mainly studies the estimation of the boundaryvalue and numerical characteristics of matrix inequalities of the Hermite matrix, whichcontains as followings:1. By estimating matrix eigenvalue mode and using the inequality theory, somenew estimates of matrix’s spread and rank of matrix are presented; the inequality isgiven as followsAnd then, its effectiveness is verified with a numerical example.2. We have obtained the following spread estimation of complex matrixpolynomial, according to the ideas of estimating matrix spread.3. Based on some scholars’ theories about positive semi-definite matrix inequalities,some kinds of Wieland-Hoffman theorem on the characteristic values of the positivesemidefinite matrix have been achieved. Further, several series of inequalities ofH lder，Cauchy and Minkowski about the trace of positive semi-definite matrix underthe Hadamard product have been proved.