P-Norm DSDD Matrix And Its Applications

Eigenvalue inclusion regions of matrices are an important topic in matrix theory and its application.Nonsingular matrices are a class of matrices with important application background.The class of nonsingular matrices is closely related to the inclusion eigenvalues regions of matrices.In this thesis,a new class of matrices,p-norm double strictly diagonally dominant matrices(shorthand for p-norm DSDD matrices),is introduced,its property is discussed,and these results are applied to study the eigenvalue inclusion regions of matrices and positive definiteness of real symmetric matrices.A new eigenvalue inclusion region of matrices is obtained and a method for determining positive definiteness of real symmetric matrices is given.Several numerical examples are given to show that the eigenvalue inclusion region in this thesis,in some cases,is contained in the famous Brauer-Cassini oval area.