'Reduced polynomial matrices' in several variables

Lomadze V.

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'Reduced polynomial matrices' in several variables

机译：“简化多项式矩阵”中的多个变量

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We define a higher-dimensional analogue of a (column) reduced polynomial matrix, called a reduced polynomial resolution, as an "exact" sequence of polynomial matrices having the "predictable degree property." A reduced polynomial resolution is associated to any linear timeinvariant differential system. It is uniquely determined (up to isomorphism) and provides a number of important integer invariants of the system.

机译：我们将（列）归约多项式矩阵的高维类似物（称为归约多项式分辨率）定义为具有“可预测度性质”的多项式矩阵的“精确”序列。降低的多项式分辨率与任何线性时不变微分系统相关。它是唯一确定的（直到同构），并提供系统的许多重要整数不变量。

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《SIAM Journal on Control and Optimization》 |2013年第4期|共16页
作者
Lomadze V.;
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原文格式 PDF
正文语种 eng
中图分类运筹学;控制论、信息论（数学理论）;
关键词
Column degree table; Complexity function; Filtered module; Graded module; Hilbert function; Jet-model; Lag table; LTID system; Reduced polynomial resolution; Strict polynomial resolution;

机译：列度表;复杂度函数;过滤模块;分级模块;希尔伯特函数;Jet模型;滞后表;LTID系统;多项式分辨率降低;严格的多项式分辨率;

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专利

1. "Reduced polynomial matrices" in several variables [J] . Lomadze V. SIAM Journal on Control and Optimization . 2013,第4期

机译：“简化多项式矩阵”中的多个变量
2. Embedding polynomial matrices of one variable [J] . Marius van dar Put, Fai Lung Tsang Indagationes Mathematicae . 2008,第4期

机译：嵌入一个变量的多项式矩阵
3. TWO VARIABLE ORTHOGONAL POLYNOMIALS ON THE BICIRCLE AND STRUCTURED MATRICES [J] . JEFFREY S. GERONIMO, HUGO WOERDEMAN SIAM Journal on Matrix Analysis and Applications . 2008,第3期

机译：双线性矩阵和结构矩阵的两个可变正交多项式
4. The definition of column reduced LAMBDA-ceneralized polynomial matrices [C] . J.Ruiz-Leon, A.Castellanos IFAC ROCOND symposium on robust control design . 2000

机译：列简化的LAMBDA中心化多项式矩阵的定义
5. Algorithms for normal forms for matrices of polynomials and Ore polynomials. [D] . Cheng, Howard. 2003

机译：多项式和Ore多项式矩阵的正规形式算法。
6. Eulerian Graphs and Polynomial Identities for Sets of Matrices [O] . Joan P. Hutchinson 1974

机译：矩阵集的欧拉图和多项式恒等式
7. On irreducible polynomials in several variables which become reducible when the variables are replaced by powers of themselves [O] . Eli Gourin 1930

机译：在几个变量中的不可约多项式，当变量被自己的电力取代时，变量是可降低的
8. Computationally Efficient Reduced Polynomial Based Algorithms for Hermitian Toeplitz Matrices. [R] . Krishna, B., Krishna, H. 1989

机译：基于计算有效简化的Hermitian Toeplitz矩阵的基于多项式的算法。

'Reduced polynomial matrices' in several variables

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