In this paper we deal with the characteristic polynomial of finite Riodan matix. We giveseveral forms of its explicit expressions. Its applications to combinatorial identities, specially to F-Lidentities, are stated.
An algorithm for simultaneous computation of the adjoint G(s) and determinant d(s) of the matrix polynomial s2J-sA 1-A 2 is presented, where J is a singular matrix. Both G(s) and d(s) are expressed relative to a basis...An algorithm for simultaneous computation of the adjoint G(s) and determinant d(s) of the matrix polynomial s2J-sA 1-A 2 is presented, where J is a singular matrix. Both G(s) and d(s) are expressed relative to a basis of Laguerre orthogonal polynomials. This algorithm is a new extension of Leverrier-Fadeev algorithm..展开更多
We present some matrix and determinant identities for the divided differences of the composite functions, which generalize the divided difference form of Faa di Bruno＇s formula. Some recent published identities can b...We present some matrix and determinant identities for the divided differences of the composite functions, which generalize the divided difference form of Faa di Bruno＇s formula. Some recent published identities can be regarded as special cases of our results.展开更多
The signless Laplacian matrix of a graph is the sum of its diagonal matrix of vertex degrees and its adjacency matrix. Li and Feng gave some basic results on the largest eigenvalue and characteristic polynomial of adj...The signless Laplacian matrix of a graph is the sum of its diagonal matrix of vertex degrees and its adjacency matrix. Li and Feng gave some basic results on the largest eigenvalue and characteristic polynomial of adjacency matrix of a graph in 1979. In this paper, we translate these results into the signless Laplacian matrix of a graph and obtain the similar results.展开更多
In this paper, we introduce a method to define generalized characteristic matrices of a defective matrix by the common form of Jordan chains. The generalized characteristic matrices can be obtained by solving a system...In this paper, we introduce a method to define generalized characteristic matrices of a defective matrix by the common form of Jordan chains. The generalized characteristic matrices can be obtained by solving a system of linear equations and they can be used to compute Jordan basis.展开更多
In this paper, we established a connection between a square matrix “A” of order “n” and a matrix defined through a new approach of the recursion relation . (where is any column matrix with n real ...In this paper, we established a connection between a square matrix “A” of order “n” and a matrix defined through a new approach of the recursion relation . (where is any column matrix with n real elements). Now the new matrix gives us a characteristic equation of matrix A and we can find the exact determination of Eigenvalues and its Eigenvectors of the matrix A. This new approach was invented by using Two eigenvector theorems along with some examples. In the subsequent paper we apply this approach by considering some examples on this invention.展开更多
文摘In this paper we deal with the characteristic polynomial of finite Riodan matix. We giveseveral forms of its explicit expressions. Its applications to combinatorial identities, specially to F-Lidentities, are stated.
文摘An algorithm for simultaneous computation of the adjoint G(s) and determinant d(s) of the matrix polynomial s2J-sA 1-A 2 is presented, where J is a singular matrix. Both G(s) and d(s) are expressed relative to a basis of Laguerre orthogonal polynomials. This algorithm is a new extension of Leverrier-Fadeev algorithm..
文摘We present some matrix and determinant identities for the divided differences of the composite functions, which generalize the divided difference form of Faa di Bruno＇s formula. Some recent published identities can be regarded as special cases of our results.
基金Foundation item： the National Natural Science Foundation of China （No. 10871204） Graduate Innovation Foundation of China University of Petroleum （No. S2008-26）.
文摘The signless Laplacian matrix of a graph is the sum of its diagonal matrix of vertex degrees and its adjacency matrix. Li and Feng gave some basic results on the largest eigenvalue and characteristic polynomial of adjacency matrix of a graph in 1979. In this paper, we translate these results into the signless Laplacian matrix of a graph and obtain the similar results.
基金Foundation item： Supported by the Science Foundation of Liuzhou Vocational Institute of Technology（2007C03）
文摘In this paper, we introduce a method to define generalized characteristic matrices of a defective matrix by the common form of Jordan chains. The generalized characteristic matrices can be obtained by solving a system of linear equations and they can be used to compute Jordan basis.
文摘In this paper, we established a connection between a square matrix “A” of order “n” and a matrix defined through a new approach of the recursion relation . (where is any column matrix with n real elements). Now the new matrix gives us a characteristic equation of matrix A and we can find the exact determination of Eigenvalues and its Eigenvectors of the matrix A. This new approach was invented by using Two eigenvector theorems along with some examples. In the subsequent paper we apply this approach by considering some examples on this invention.
基金Supported by the National Natural Science Foundation of China(2 0 0 0 CG0 1 0 3) the Fund of"The Developing Program for Outstanding Person"in NPUS & T Innovation Foundation for Young Teachers of Northwestern Polytechnical University.
文摘In this paper, the spectrum and characteristic polynomial for a special kind of symmetric block circulant matrices are given.
基金Supported by the National Natural Science Foundation of China(10871166)the Science Foundation of Shanghai Education Com-mittee (05QZ01)the Financial Grant of Shanghai Department of Finance (1138IA0005 and 1139IA0013)
