In this paper,the GH-congruence canonical forms of positive semidefinite and definte inite and definite(need not be self-conjugate)quaternion matrices are given,and a neccessary and sufficientcondition of GH-congruenc...In this paper,the GH-congruence canonical forms of positive semidefinite and definte inite and definite(need not be self-conjugate)quaternion matrices are given,and a neccessary and sufficientcondition of GH-congruence for two positive semidifinite(definite)quaternion matrices isgiven also.Then simultaneous GH-congruence reduced forms for two self-conjugate matri-ces and some result about the simultaneous GH-congruence diagonalization of quaternionmatrices are obtained.展开更多
A closed-form solution to the linear matrix equation AX-EXF = BY with X and Y unknown and matrix F being in a companion form is proposed, and two equivalent forms of this solution are also presented. The results provi...A closed-form solution to the linear matrix equation AX-EXF = BY with X and Y unknown and matrix F being in a companion form is proposed, and two equivalent forms of this solution are also presented. The results provide great convenience to the computation and analysis of the solutions to this class of equations, and can perform important functions in many analysis and design problems in descriptor system theory. The results proposed here are parallel to and more general than our early work about the linear matrix equation AX-XF = BY .展开更多
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...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 matrix is similar to Jordan canonical form over the complex field and the rational canonical form over a number field, respectively. In this paper, we further study the rational canonical form of a matrix over any n...A matrix is similar to Jordan canonical form over the complex field and the rational canonical form over a number field, respectively. In this paper, we further study the rational canonical form of a matrix over any number field. We firstly discuss the elementary divisors of a matrix over a number field. Then, we give the quasi-rational canonical forms of a matrix by combining Jordan and the rational canonical forms. Finally, we show that a matrix is similar to its quasi-rational canonical forms over a number field.展开更多
Mg matrix composites with SiC particles ranging from 5vol%-25vol% were prepared using stirring casting method. Die casting, squeezing casting, and extrusion were applied for inhibiting or eliminating the defects such ...Mg matrix composites with SiC particles ranging from 5vol%-25vol% were prepared using stirring casting method. Die casting, squeezing casting, and extrusion were applied for inhibiting or eliminating the defects such as gas porosity and shrinkage void. Through die casting and squeezing casting, most of the defects in Mg matrix composites could be eliminated, but the mechanical properties were improved limitedly. On the other hand, after hot extrusion, not only most of the defects of as-cast composites ingots were eliminated, but also the mechanical properties were improved markedly. With the addition of SiC, the tensile strength, yield strength and elastic modulus of as extrusion SiCp/AZ61 composites increased remarkably, and the elongation decreased obviously.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.
The aim of this paper deals with the study of the Horn matrix function of two complex variables. The convergent properties, an integral representation of H2(A,A′,B,B′;C;z,w) is obtained and recurrence matrix relatio...The aim of this paper deals with the study of the Horn matrix function of two complex variables. The convergent properties, an integral representation of H2(A,A′,B,B′;C;z,w) is obtained and recurrence matrix relations are given. Some result when operating on Horn matrix function with the differential operator D and a solution of certain partial differential equations are established. The Hadamard product of two Horn’s matrix functions is studied, certain results as, the domain of regularity, contiguous functional relations and operating with the differential operator D and D2 are established.展开更多
文摘In this paper,the GH-congruence canonical forms of positive semidefinite and definte inite and definite(need not be self-conjugate)quaternion matrices are given,and a neccessary and sufficientcondition of GH-congruence for two positive semidifinite(definite)quaternion matrices isgiven also.Then simultaneous GH-congruence reduced forms for two self-conjugate matri-ces and some result about the simultaneous GH-congruence diagonalization of quaternionmatrices are obtained.
基金supported by the Major Program of National Nat-ural Science Foundation of China (No. 60710002) Program for Changjiang Scholars and Innovative Research Team in University
文摘A closed-form solution to the linear matrix equation AX-EXF = BY with X and Y unknown and matrix F being in a companion form is proposed, and two equivalent forms of this solution are also presented. The results provide great convenience to the computation and analysis of the solutions to this class of equations, and can perform important functions in many analysis and design problems in descriptor system theory. The results proposed here are parallel to and more general than our early work about the linear matrix equation AX-XF = BY .
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.
文摘A matrix is similar to Jordan canonical form over the complex field and the rational canonical form over a number field, respectively. In this paper, we further study the rational canonical form of a matrix over any number field. We firstly discuss the elementary divisors of a matrix over a number field. Then, we give the quasi-rational canonical forms of a matrix by combining Jordan and the rational canonical forms. Finally, we show that a matrix is similar to its quasi-rational canonical forms over a number field.
基金Funded by the Program for New Century Excellent Talents in University(NCET-12-1040)the National Natural Science Foundation of China(Nos.50901048 and 51174143)+2 种基金the Key Project of Chinese Ministry of Education(No.2012017)the Program Foundation of Ministry of Education of China(No.20101402110008)Natural Science Foundation of Shanxi(No.2010021022-5)
文摘Mg matrix composites with SiC particles ranging from 5vol%-25vol% were prepared using stirring casting method. Die casting, squeezing casting, and extrusion were applied for inhibiting or eliminating the defects such as gas porosity and shrinkage void. Through die casting and squeezing casting, most of the defects in Mg matrix composites could be eliminated, but the mechanical properties were improved limitedly. On the other hand, after hot extrusion, not only most of the defects of as-cast composites ingots were eliminated, but also the mechanical properties were improved markedly. With the addition of SiC, the tensile strength, yield strength and elastic modulus of as extrusion SiCp/AZ61 composites increased remarkably, and the elongation decreased obviously.
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The aim of this paper deals with the study of the Horn matrix function of two complex variables. The convergent properties, an integral representation of H2(A,A′,B,B′;C;z,w) is obtained and recurrence matrix relations are given. Some result when operating on Horn matrix function with the differential operator D and a solution of certain partial differential equations are established. The Hadamard product of two Horn’s matrix functions is studied, certain results as, the domain of regularity, contiguous functional relations and operating with the differential operator D and D2 are established.
