The theory of Schur complement plays an important role in many fields such as matrix theory, control theory and computational mathematics. In this paper, some new estimates of diagonally, α-diagonally and product α-...The theory of Schur complement plays an important role in many fields such as matrix theory, control theory and computational mathematics. In this paper, some new estimates of diagonally, α-diagonally and product α-diagonally dominant degree on the Schur complement of matrices are obtained, which improve some relative results. As an application, we present several new eigenvalue inclusion regions for the Schur complement of matrices. Finally, we give a numerical example to illustrate the advantages of our derived results.展开更多
The graph theory of eigenvalue problem also shows a kind of relation existing in a determinant, from which some inferences were made by this paper. The first corollary expresses how a change in a pair of linking lines...The graph theory of eigenvalue problem also shows a kind of relation existing in a determinant, from which some inferences were made by this paper. The first corollary expresses how a change in a pair of linking lines in a graph will affect the eigenpolynomial （EP） corresponding to it. The second one proves i—j is an algebraic展开更多
文摘The theory of Schur complement plays an important role in many fields such as matrix theory, control theory and computational mathematics. In this paper, some new estimates of diagonally, α-diagonally and product α-diagonally dominant degree on the Schur complement of matrices are obtained, which improve some relative results. As an application, we present several new eigenvalue inclusion regions for the Schur complement of matrices. Finally, we give a numerical example to illustrate the advantages of our derived results.
文摘The graph theory of eigenvalue problem also shows a kind of relation existing in a determinant, from which some inferences were made by this paper. The first corollary expresses how a change in a pair of linking lines in a graph will affect the eigenpolynomial （EP） corresponding to it. The second one proves i—j is an algebraic
