A Survey on Semi-Tensor Product of Matrices
查看参考文献42篇
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文摘
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Semi-tensor product of matrices is a generalization of conventional matrix product for the case when the two factor matrices do not meet the dimension matching condition. It was firstly proposed about ten years ago. Since then it has been developed and applied to several different fields. In this paper we will first give a brief introduction. Then give a survey on its applications to dynamic systems, to logic, to differential geometry, to abstract algebra, respectively. |
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来源
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Journal of Systems Science and Complexity
,2007,20(2):304-322 【核心库】
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DOI
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10.1007/s11424-007-9027-0
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关键词
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Abstract algebra
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differential geometry
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dynamic systems
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logic
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semi-tensor product
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地址
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Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080
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语种
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英文 |
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文献类型
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研究性论文 |
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ISSN
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1009-6124 |
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学科
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数学 |
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基金
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国家自然科学基金
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文献收藏号
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CSCD:3144288
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参考文献 共
42
共3页
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1.
R A Horn.
Topics in Matrix Analysis(Vol. 1),1991
|
CSCD被引
1
次
|
|
|
|
|
2.
R A Horn.
Topics in Matrix Analysis(Vol. 2),1991
|
CSCD被引
1
次
|
|
|
|
|
3.
D Cheng.
Matrix and Polynomial Approach to Dynamic Control Systems,2002
|
CSCD被引
3
次
|
|
|
|
|
4.
D Cheng.
Semi-tensor Product of Matrices--Theory and Applications,2007
|
CSCD被引
2
次
|
|
|
|
|
5.
J R Magnus.
Matrix Differential Calculus with Applications in Statistics and Econometrics(Revised Ed. ),1999
|
CSCD被引
1
次
|
|
|
|
|
6.
W M Boothby.
An Introduction to Differential Manifolds and Riemannian Geometry(2nd Ed. ),1986
|
CSCD被引
1
次
|
|
|
|
|
7.
L Zhang. The general structure of cubic matrices(in Chinese).
Sys. Sci. Math. Sci.,2005,25(8):439-450
|
CSCD被引
1
次
|
|
|
|
|
8.
J G Zaborszky. On the phase protraits of a class of large nonlinear dynamic systems such as the power systems.
IEEE Trans. Autom. Contr.,1998,33(1):4-15
|
CSCD被引
1
次
|
|
|
|
|
9.
H D Chiang. Stability regions of nonlinear autonomous dynamical systems.
IEEE Trans. Automat. Contr.,1988,33(1):16-27
|
CSCD被引
59
次
|
|
|
|
|
10.
D Cheng. Calculation of stability region.
Proc. 42nd IEEE Conference on Decision and Control 2003,2003:5615-5620
|
CSCD被引
1
次
|
|
|
|
|
11.
D Cheng.
Int. J. Robust and Nonlinear Control,2004,14:773-788
|
CSCD被引
2
次
|
|
|
|
|
12.
D Cheng. Semi-tensor product of matrices and its applications to dynamic systems,New Directions and Applications in Control Theory.
Lecture Notes in Control and Information Sciences,2005:61-79
|
CSCD被引
2
次
|
|
|
|
|
13.
J Ma. On complexity of power systems.
J. Sys. Sci. & Complexity,2003,16(3):391-403
|
CSCD被引
3
次
|
|
|
|
|
14.
J Ma. Approximation of the boundary of power system stability region based on semi-tensor theory, Part One:theoretical basis(in Chinese).
Auto. Elec. Power Sys.,2006,30(10):1-5
|
CSCD被引
4
次
|
|
|
|
|
15.
J Ma. Approximation of the boundary of power system stability region based on semi-tensor theory, Part Two:application(in Chinese).
Auto. Elec. Power Sys.,2006,30(11):1-6
|
CSCD被引
4
次
|
|
|
|
|
16.
F Zhang.
Matrix Theory, Basic Results and Techniques,1999
|
CSCD被引
3
次
|
|
|
|
|
17.
D Cheng. Non-regular feedback linearization of nonlinear systems via a normal form algorithm.
Automatica,2004,40(3):439-447
|
CSCD被引
5
次
|
|
|
|
|
18.
J Zhong. New results on non-regular linearization of nonlinear systems.
Int. J. Contr.:accepted
|
CSCD被引
1
次
|
|
|
|
|
19.
D Cheng. Nonlinear systems possessing linear symmetry.
Int. J. Robust Nonli. Contr.:to appear
|
CSCD被引
1
次
|
|
|
|
|
20.
J E Humphreys.
Introduction to Lie Algebras and Representation Theory,1972
|
CSCD被引
68
次
|
|
|
|
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