Study On Frobenius Norm Inequalities And Subadditivity Of Matrices

For a long time, matrix inequalities is an important domain of algebra research. Matrix inequalities’ research is very active no matter in theory or in practical application. In recent years, there are many matrix inequalities based on classical numerical inequalities, and its’ promotion and application has become a hot topic in matrix theory. This article mainly do some exploring researches on the matrix norm inequalities,and reach some conclusions about the generalization and refinement of the inequalities. In this paper, the research content and innovation points mainly includes:(1) We present a generalization of the Cauchy–Schwarz type matrix norm inequality under Frobenius norm;(2) When A,B are positive semi-definite matrixes, we give a new generalization of the Cauchy–Schwarz type matrix norm inequality by adding coefficient r;(3) We present two reverse Heinz type numerical inequalities by use the relationship between Young inequality and Heinz means, and based on this we obtain a Frobenius norm inequalities;(4) We obtain two differences type inequalities, and based on this conclusion we prove that the Heinz type inequality mentioned in(3) is better than some of the existing literature results;(5) By using the dominant theory of matrix singular value, we present a further refinement of subadditivity matrix norm inequality, and we get two Chebyshev type matrice norm inequalities under the exchangeability of the matrixes.