New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations a...New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations and provide all Jordan basesby which the Jordan canonical form is constructed. Accordingly, they can result in thecelebrated Jordan theorem and the third decomposition theorem of space directly. and,moreover, they can give a new deep insight into the exquisite and subtle structure ofthe Jordan form. The latter indicates that the Jordan canonical form of a complexlinear transformation is an invariant structure associated with double arbitrary. choices.展开更多
Several important properties of a kind of random symplectic matrix used by A. Bunse-Gerstner and V. Mehrmann are studied and the following results are obtained: 1) It can be transformed to Jordan canonical form by ort...Several important properties of a kind of random symplectic matrix used by A. Bunse-Gerstner and V. Mehrmann are studied and the following results are obtained: 1) It can be transformed to Jordan canonical form by orthogonal similar transformation; 2) Its condition number is a constant; 3) The condition number of it is about 2.618.展开更多
Every matrix is similar to a matrix in Jordan canonical form,which has very important sense in the theory of linear algebra and its engineering application.For a matrix with multiplex eigenvalues,an algorithm based on...Every matrix is similar to a matrix in Jordan canonical form,which has very important sense in the theory of linear algebra and its engineering application.For a matrix with multiplex eigenvalues,an algorithm based on the singular value decomposition(SVD) for computing its eigenvectors and Jordan canonical form was proposed.Numerical simulation shows that this algorithm has good effect in computing the eigenvectors and its Jordan canonical form of a matrix with multiplex eigenvalues.It is superior to MATLAB and MATHEMATICA.展开更多
In this paper,using the Jordan canonical form of the Pascal matrix Pn,we present a new approach for inverting the Pascal matrix plus a scalar Pn+aIn for arbitrary real number a≠1.
In this paper we present some new absolute and relative perturbation bounds for the eigenvalue for arbitrary matrices, which improves some recent results. The eigenvalue inclusion region is also discussed.
文摘New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations and provide all Jordan basesby which the Jordan canonical form is constructed. Accordingly, they can result in thecelebrated Jordan theorem and the third decomposition theorem of space directly. and,moreover, they can give a new deep insight into the exquisite and subtle structure ofthe Jordan form. The latter indicates that the Jordan canonical form of a complexlinear transformation is an invariant structure associated with double arbitrary. choices.
文摘Several important properties of a kind of random symplectic matrix used by A. Bunse-Gerstner and V. Mehrmann are studied and the following results are obtained: 1) It can be transformed to Jordan canonical form by orthogonal similar transformation; 2) Its condition number is a constant; 3) The condition number of it is about 2.618.
文摘Every matrix is similar to a matrix in Jordan canonical form,which has very important sense in the theory of linear algebra and its engineering application.For a matrix with multiplex eigenvalues,an algorithm based on the singular value decomposition(SVD) for computing its eigenvectors and Jordan canonical form was proposed.Numerical simulation shows that this algorithm has good effect in computing the eigenvectors and its Jordan canonical form of a matrix with multiplex eigenvalues.It is superior to MATLAB and MATHEMATICA.
基金Supported by the Natural Science Foundation of Gansu Proveince（1010RJZA049）
文摘In this paper,using the Jordan canonical form of the Pascal matrix Pn,we present a new approach for inverting the Pascal matrix plus a scalar Pn+aIn for arbitrary real number a≠1.
文摘In this paper we present some new absolute and relative perturbation bounds for the eigenvalue for arbitrary matrices, which improves some recent results. The eigenvalue inclusion region is also discussed.
