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jordan标准形的
相关语句
  jordan canonical form
     Tbese new objects yield a new result for the decomposition of complex vector spaces relative to complex linear transformations and provide all Jordan bases by which the Jordan canonical form is constructed.
     这些新对象给出复向量空间关于复线性变换分解的新结果且给出构造Jordan标准形的所有Jordan基。
短句来源
     Generalized Eigenspaces and Jordan Chains:A New Approach to the Jordan Canonical Form
     广义特征子空间与Jordan链:构造Jordan标准形的一个新途径
短句来源
     Study the Existence of the Jordan Canonical Form of a Complex Matrix from the Module Viewpoint
     模观点下看矩阵Jordan标准形的存在性
短句来源
     If A is a n×n matrix of a field F,it is argued that the least polynomial of the adjoint matrices of A can be expressed by using the least polynomial of A; and it is also shown that the Jordan canonical form of the adjoint matrices can be expressed by using the Jordan canonical form of A. Methods are given.
     A是数域F上n阶方阵,文中给出用A的最小多项式来表示A的伴随阵的最小多项式的表达式,以及由A的Jordan标准形表示出A之伴随阵的Jordan标准形的方法。
短句来源
     A concept of companion vector was introduced, and a definition of rank of quaternion matrix was given, and a simple proof of Jordan canonical form of matrices over quaternion field was studied.
     引入了友向量的概念 ,给出了四元数矩阵的秩的一种定义方法和四元数矩阵Jordan标准形的一种简单证明和算法 .
短句来源
更多       
  the jordan canonical form
     Tbese new objects yield a new result for the decomposition of complex vector spaces relative to complex linear transformations and provide all Jordan bases by which the Jordan canonical form is constructed.
     这些新对象给出复向量空间关于复线性变换分解的新结果且给出构造Jordan标准形的所有Jordan基。
短句来源
     Generalized Eigenspaces and Jordan Chains:A New Approach to the Jordan Canonical Form
     广义特征子空间与Jordan链:构造Jordan标准形的一个新途径
短句来源
     Study the Existence of the Jordan Canonical Form of a Complex Matrix from the Module Viewpoint
     模观点下看矩阵Jordan标准形的存在性
短句来源
     If A is a n×n matrix of a field F,it is argued that the least polynomial of the adjoint matrices of A can be expressed by using the least polynomial of A; and it is also shown that the Jordan canonical form of the adjoint matrices can be expressed by using the Jordan canonical form of A. Methods are given.
     A是数域F上n阶方阵,文中给出用A的最小多项式来表示A的伴随阵的最小多项式的表达式,以及由A的Jordan标准形表示出A之伴随阵的Jordan标准形的方法。
短句来源
     In the paper,we define the minimal polynomial of linear transformation (matrix) and discuss some of its properties,provide the method for the transition matrix,then we obtain a simpler proof of the Jordan Canonical form.
     该文首先定义线性变换 (矩阵 )的最小多项式 ,讨论它的若干性质 ,并给出求过渡矩阵的方法 ,从而得到 Jordan标准形的一种比较简洁的证明 :
短句来源
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  “jordan标准形的”译为未确定词的双语例句
     CALCULUS OF JORDAN CANONICAL MATRIX
     矩阵Jordan标准形的计算
短句来源
     Another method to solve the Jordan Standard form of matrix A
     求矩阵A的Jordan标准形的另一方法
短句来源
     A New Algorithm for the Similarity Transformation of a Matrix to Its Jordan Canonical Matrix
     求矩阵到其Jordan标准形的过渡矩阵的新算法
短句来源
     This paper puts forward another method to solve the Jordan standard form of matrix A: uses the calculation of the rank of the martrix (λ iE-A) P to get the orders and numbers of Jordan matrix about the charcteristic root (λ i , then solves the Jordan standard form of matrix A.
     本文提出了求矩阵 A的 Jordan标准形的另一方法 :利用 rank(λi(E- A) P 的结果 ,得出了对应于特征值 (λi 的 Jordan块的阶数和个数 ,然后求出矩阵 A的 Jordan标准形
短句来源
     On Rooting Matrices for the Jordan's Normal Form Matrix of Characteristic Root 0
     特征根全为0的Jordan标准形的根矩阵
短句来源
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  jordan canonical form
These new objects yield a new result for the decomposition of complex vector spaces relative to complex linear transformations and provide all Jordan bases by which the Jordan canonical form is constructed.
      
The latter indicates that the Jordan canonical form of a complex linear transformation is an invariant structure associated with double arbitrary choices.
      
Using quaternion multiplication and the double determinant theory over quaternion field, we proved that an arbitrary quaternion square matrix is similar to a unique Jordan canonical form indicated by its principal characteristic values.
      
Mehrmann are studied and the following results are obtained: 1) It can be transformed to Jordan canonical form by orthogonal similar transformation; 2) Its condition number is a constant; 3) The condition number of it is about 2.618.
      
All the eigensolutions and Jordan canonical form eigensolutions for zero eigenvalue of the Hamiltonian operator matrix are solved in detail, and their physical meanings are showed clearly.
      
更多          
  the jordan canonical form
These new objects yield a new result for the decomposition of complex vector spaces relative to complex linear transformations and provide all Jordan bases by which the Jordan canonical form is constructed.
      
The latter indicates that the Jordan canonical form of a complex linear transformation is an invariant structure associated with double arbitrary choices.
      
The stability of the non-trivial steady-state solution is studied for cases in which the corresponding linear autonomous system of equations, obtained by setting ? = o, is in the Jordan canonical form with two equal non-zero characteristic values.
      
The Moore-Penrose and group inverse of square matrices and the Jordan canonical form
      
This paper is a continuation of the paper [3], where the first two Penrose's equations are solved for a square matrix, which is transformed into the Jordan canonical form.
      


Let A be any nxn matrix and J, its Jordan canonical form. A nonsingular matrix T which satisfies.T-1AT=J, is called a transformation matrix.In this paper, an algorithm is developed for obtaining the Jordan canonical form J of matrix A and for producing simultaneously a transformation matrix T when all the different eigenvalues of A are known.In [2], a different algorithm, is also proposed. Unfortunately, some mistakes have been found there. The basic idea of [2] is described as follows: suppose that V is the...

Let A be any nxn matrix and J, its Jordan canonical form. A nonsingular matrix T which satisfies.T-1AT=J, is called a transformation matrix.In this paper, an algorithm is developed for obtaining the Jordan canonical form J of matrix A and for producing simultaneously a transformation matrix T when all the different eigenvalues of A are known.In [2], a different algorithm, is also proposed. Unfortunately, some mistakes have been found there. The basic idea of [2] is described as follows: suppose that V is the linear space of n dimensions , is an eigenvalue of A and B = A-I.Denoting V0= { 0 }, W0= V, then one may successively construct spaces Vt and Wi in the way that Wi= V1+1 + Wi+1, Vi+1 Wi+ 1 = { 0 }. Vi+1 = {xWi| Bx Vi} and the process may terminate when dim Vm+1= 0. [2] says that V'm=V1+V2 +defines the subspace of V, which corresponds to the eigenvalue of A, and V can be written as the direct sum of invariant subspaces V= V'm Wm. This is not true. For example, if which satisfies all the above conditions, i.e.,We take W1 = V1+W1=V and V1 W1= {0}. From W1 we can obtain the space V2If we take W2 as the spaces and it satisfies the conditions that W1= V2+W2And V2 W2 = {0}, then dim V3= 0.In fact, V3= {x W2|Bx V2}. Since x W2, x must be of the form aand Bx = On another hand, any vector y V2, must be of the form Thus, if Bx V2, a must be zero, and it follows that dim Vs= 0.V2' = V1 + V2 = is an invariant subapace, but W2 = > is not.The algorithm proposed in this paper gives corrections to the mistakes of [2]. Furthermore it is proved that for any matrix A, the matrix T produced by the computations with our algorithm is indeed a transformation matrix.

本文给出一种计算任意复方阵的Jordan标准形的变换矩阵的算法,并证明按照给出的算法计算结果得到的一个矩阵确是所要求的Jordan标准形的变换矩阵。

This paper discusses'the problem of Jordan Canonical form of Matrix.In section 1 the three elementary lemmas are proved.Then on the basis of this result,the existence and uniqueness theorem of the Jordan Canonical form is derived in section 2.Finally,in section 3 we discuss a method for finding the transformation matrix which transforms a given matrix into the Jordan Canonical form.

本文讨论矩阵的Jordan标准形问题。第一节证明了三个基本引理。然后,在此基础上,第二节导出了矩阵Jordan标准形的存在和唯一性定理。最后,在第三节,讨论了将给出的矩阵变换成Jordan标准形的变换矩阵的求法。

We first give a simplified proof of the piimairy decomposirion theorem of the vector (?)space Then we have the brief deduction of the existence and uniqueness theorem of Jordan form.

本文先将线性空间基本分解定理的证明进行了简化,然后得出Jordan标准形存在唯一性定理的简明推导。

 
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