By using the Smith normal form of polynomial matrix and algebraic methods, this paper discusses the solvability for the linear matrix equation A iXB i=C over a field, and obtains the explicit formulas of general sol...By using the Smith normal form of polynomial matrix and algebraic methods, this paper discusses the solvability for the linear matrix equation A iXB i=C over a field, and obtains the explicit formulas of general solution or unique solution.展开更多
A brief introduction is given to the topic of Smith normal forms of incidence matrices. A general discussion of techniques is illustrated by some classical examples. Some recent advances are described and the limits o...A brief introduction is given to the topic of Smith normal forms of incidence matrices. A general discussion of techniques is illustrated by some classical examples. Some recent advances are described and the limits of our current understanding are indicated.展开更多
A connected graph, whose blocks are all cliques （of possibly varying sizes）, is called a block graph. Let D（G） be its distance matrix. In this note, we prove that the Smith normal form of D（G） is independent of ...A connected graph, whose blocks are all cliques （of possibly varying sizes）, is called a block graph. Let D（G） be its distance matrix. In this note, we prove that the Smith normal form of D（G） is independent of the interconnection way of blocks and give an explicit expression for the Smith normal form in the case that all cliques have the same size, which generalize the results on determinants.展开更多
The zero coprime system equivalence is one of important research in the theory of multidimensional system equivalence,and is closely related to zero coprime equivalence of multivariate polynomial matrices.We first dis...The zero coprime system equivalence is one of important research in the theory of multidimensional system equivalence,and is closely related to zero coprime equivalence of multivariate polynomial matrices.We first discuss the relation between zero coprime equivalence and unimodular equivalence for polynomial matrices.Then,we investigate the zero coprime equivalence problem for several classes of polynomial matrices,some novel findings and criteria on reducing these matrices to their Smith normal forms are obtained.Finally,an example is provided to illustrate the main results.展开更多
基金the NSF of Hunan Province and the Science and Technology Development Foundation of Xiangtan Polytechnic University
文摘By using the Smith normal form of polynomial matrix and algebraic methods, this paper discusses the solvability for the linear matrix equation A iXB i=C over a field, and obtains the explicit formulas of general solution or unique solution.
基金supported by the Simons Foundation(Grant No.#204181)
文摘A brief introduction is given to the topic of Smith normal forms of incidence matrices. A general discussion of techniques is illustrated by some classical examples. Some recent advances are described and the limits of our current understanding are indicated.
基金supported by the National Natural Science Foundation of China(Nos.11501188,11326057,11171102)by Aid program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province
文摘A connected graph, whose blocks are all cliques （of possibly varying sizes）, is called a block graph. Let D（G） be its distance matrix. In this note, we prove that the Smith normal form of D（G） is independent of the interconnection way of blocks and give an explicit expression for the Smith normal form in the case that all cliques have the same size, which generalize the results on determinants.
基金Supported by the National Natural Science Foundation of China(12271154)the Natural Science Foundation of Hunan Province(2022JJ30234)the Postgraduate Scientific Research Innovation Project of Hunan Province(CX20231032)。
文摘The zero coprime system equivalence is one of important research in the theory of multidimensional system equivalence,and is closely related to zero coprime equivalence of multivariate polynomial matrices.We first discuss the relation between zero coprime equivalence and unimodular equivalence for polynomial matrices.Then,we investigate the zero coprime equivalence problem for several classes of polynomial matrices,some novel findings and criteria on reducing these matrices to their Smith normal forms are obtained.Finally,an example is provided to illustrate the main results.
基金Program Sponsored by Scientific Innovation Research of College Graduate in Jiangsu Province(CXZZ_0163)Scientific Research Foundation of Graduate School of Southeast University(YBJJ1140)
