Two n × n complex matrices A and B are said to be consimilar if S?1AS = B for some nonsingular n × n complex matrix S. This paper, by means of real representation of a complex matrix, studies problems of red...Two n × n complex matrices A and B are said to be consimilar if S?1AS = B for some nonsingular n × n complex matrix S. This paper, by means of real representation of a complex matrix, studies problems of reducing a given n × n complex matrix A to triangular or diagonal form by consimilarity, not only gives necessary and su?cient conditions for contriangularization and condiagonalization of a complex matrix, but also derives an algebraic technique of reducing a matrix to triangular or diagonal form by consimilarity.展开更多
This paper aims to present, in a unified manner, algebraic techniques for linear equations which are valid on both the algebras of quaternions and split quaternions. This paper, introduces a concept of v-quaternion, s...This paper aims to present, in a unified manner, algebraic techniques for linear equations which are valid on both the algebras of quaternions and split quaternions. This paper, introduces a concept of v-quaternion, studies the problem of v-quaternionic linear equations by means of a complex representation and a real representation of v-quaternion matrices, and gives two algebraic methods for solving v-quaternionic linear equations. This paper also gives a unification of algebraic techniques for quaternionic and split quaternionic linear equations in quaternionic and split quaternionic mechanics.展开更多
This paper aims to present, in a unified manner, the algebraic techniques of eigen-problem which are valid on both the quaternions and split quaternions. This paper studies eigenvalues and eigenvectors of the v-quater...This paper aims to present, in a unified manner, the algebraic techniques of eigen-problem which are valid on both the quaternions and split quaternions. This paper studies eigenvalues and eigenvectors of the v-quaternion matrices by means of the complex representation of the v-quaternion matrices, and derives an algebraic technique to find the eigenvalues and eigenvectors of v-quaternion matrices. This paper also gives a unification of algebraic techniques for eigenvalues and eigenvectors in quaternionic and split quaternionic mechanics.展开更多
Kennaugh＇s pseudo-eigenvalue equation is a basic equation that plays an extremely important role in radar polarimetry. In this paper, by means of real representation, we first present a necessary and sufficient condi...Kennaugh＇s pseudo-eigenvalue equation is a basic equation that plays an extremely important role in radar polarimetry. In this paper, by means of real representation, we first present a necessary and sufficient condition for the general Kennaugh＇s pseudo-eigenvalue equation having a solution, characterize the explicit form of the solution, and then study the solution of Kennaugh＇s pseudo-eigenvalue equation. At last, we propose a new technique for finding the coneigenvalues and coneigenvectors of a complex matrix under appropriate conditions in radar polarimetry.展开更多
基金This paper is supported by the National Natural Science Foundation of China (10371044).
文摘Two n × n complex matrices A and B are said to be consimilar if S?1AS = B for some nonsingular n × n complex matrix S. This paper, by means of real representation of a complex matrix, studies problems of reducing a given n × n complex matrix A to triangular or diagonal form by consimilarity, not only gives necessary and su?cient conditions for contriangularization and condiagonalization of a complex matrix, but also derives an algebraic technique of reducing a matrix to triangular or diagonal form by consimilarity.
文摘This paper aims to present, in a unified manner, algebraic techniques for linear equations which are valid on both the algebras of quaternions and split quaternions. This paper, introduces a concept of v-quaternion, studies the problem of v-quaternionic linear equations by means of a complex representation and a real representation of v-quaternion matrices, and gives two algebraic methods for solving v-quaternionic linear equations. This paper also gives a unification of algebraic techniques for quaternionic and split quaternionic linear equations in quaternionic and split quaternionic mechanics.
文摘This paper aims to present, in a unified manner, the algebraic techniques of eigen-problem which are valid on both the quaternions and split quaternions. This paper studies eigenvalues and eigenvectors of the v-quaternion matrices by means of the complex representation of the v-quaternion matrices, and derives an algebraic technique to find the eigenvalues and eigenvectors of v-quaternion matrices. This paper also gives a unification of algebraic techniques for eigenvalues and eigenvectors in quaternionic and split quaternionic mechanics.
基金Acknowledgements We wish to express our gratitude to the anonymous referees for their helpful comments and suggestions, which improved the presentation of this paper. This work was supported in part by the National Natural Science Foundations of China （Grant Nos. 11171226, 11171343, 11001144） and the Natural Science Foundation of Shandong Province （ZR2010AM014）.
文摘Kennaugh＇s pseudo-eigenvalue equation is a basic equation that plays an extremely important role in radar polarimetry. In this paper, by means of real representation, we first present a necessary and sufficient condition for the general Kennaugh＇s pseudo-eigenvalue equation having a solution, characterize the explicit form of the solution, and then study the solution of Kennaugh＇s pseudo-eigenvalue equation. At last, we propose a new technique for finding the coneigenvalues and coneigenvectors of a complex matrix under appropriate conditions in radar polarimetry.
