Exploring And Promotion Of Minkowski Inequality Of The Determinant Of A Matrix

The Minkowski inequality of determinant of matrix has been used in theoriesand practice. For example, the famous Pedoe inequality, Hadamard inequalitycan be launched from it simply.In recent years, Minkowski inequality of the de-terminant of a matrix has attracted the attention of scholars home and abroad.They have di?erent researches and extensions and have got fruitful results.In this thesis, combining with Ho¨lder inequality, the discrete form of minkowskiinequality, we will use the knowledge of matrix theory and analytical skills todiscuss and study the necessary and su?cient conditions of the equality of gener-alized minkowski inequality. Furthermore, we have improved the known results.The main contents in the thesis is the following areas:In chapter one, we first present some background knowledge and recent worksfor matrix and minkowski inequality. Then we introduce some basic symbols anddefinitions used in this thesis.In chapter two, combining with the promotion of the H (o|¨)lder inequality andminkowski inequality, we will use monotonicity of the constructor and inequalityoperators to study generalized minkowski inequality as well as the necessary andsu?cient conditions of the equality of it. It is also the basis of chapter three.In chapter three, in case of chapter two and some of the recent literatures, Anew improvement of minkowski inequality is established in positive definite ma-trix, generalized positive definite matrix, and complex positive definite matrix bythe nature of the matrix eigenvalue and the principle of unitary diagonalization.Moreover, we discuss the the conditions of the equality of generalized minkowskiinequalities. And some numerical examples are given to verify their e?ectiveness.