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jordan标准
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  jordan canonical
     We discussed the invertible matrix W_o relating a matrix A over a field F to its Jordan canonical matrix, and provided, in theory, a elementary method of obtaining W_o.
     讨论了域F上矩阵A到它的Jordan标准形所关联的可逆矩阵W_0,在理论上给出了求W_0的一种初等方法.
短句来源
     CALCULUS OF JORDAN CANONICAL MATRIX
     矩阵Jordan标准形的计算
短句来源
     THE JORDAN CANONICAL FORM OF A REAL RANDOM MATRIX
     实随机矩阵的Jordan标准
短句来源
     Aim To discuss the dimensions of solution space for Linear matrix equations AX+XB=0,X+AXB=0.Methods Using the blocking methed and the Jordan Canonical form of matrices.
     目的给出AX+XB=0,X+AXB=0型矩阵方程的解空间维数。 方法运用分块矩阵和Jordan标准形对解空间维数进行讨论。
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
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  jordan standard
     About to the m order matrix equation: X m+a 1X m-1 +…a m-1 X+a mE n=0,E n is n order unit matrix , a 1,a 2,…,a m∈R,X∈C n×n . This paper used the relative conclusion of zeroize palynomial,ninimum palynomial and the Jordan standard form of the matrix,discusses all the possible answer of this equation.
     关于m次矩阵方程Xm+a1Xm-1+…+am-1X+amEn=0,其中En是n阶单位矩阵,a1,a2,…,am∈R,X∈Cn×n,本文利用矩阵的化零多项式,最小多项式的相关结论以及Jordan标准形分解,讨论了该方程的所有可能解.
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
     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
短句来源
     Existence of Module Method Demonstrationof Jordan Standard Form of Matrix
     矩阵的Jordan标准形的存在性的模论方法证明
短句来源
     it studied the specific structure of γ(A), gived the general formula (Thcorem 2) on elements of abelian group γ(A) of A matrix and obtained a new formula on general solution of matrix equation AX=XA (Theorem 3), obtained the rules on how ic write directly the general formula and general solution with Jordan standard form of matrix A and B as well.
     研究了γ(4)的具体结构,给出了矩阵A可换群γ(A)元通式(定理2)、获得了矩阵方程 AX=XB的通解公式(定理 3),以及由 A、B的 Jordan标准形直接写出该通式、通解的规则。
短句来源
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  jordan ' s normal
     Jordan's Normal Form of 2-nilpotent Matrix
     2-幂零矩阵的Jordan标准
短句来源
     The application of matrix Jordan's normal form
     矩阵Jordan标准形及其应用
短句来源
     Some applications of the matrix Jordan's normal form in advanced algebra theory are probed into.
     探讨了矩阵Jordan标准形在高等代数理论中的若干应用.
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
     We give the structure of the stable group of the Jordan's normal form of 2-nilpotent matrices under the similarity transformation. One construction of Cartesian authentication codes from 2-nilpotent matrices over a finite fields is presented and its size parameters are computed.
     给出 2 -幂零矩阵的Jordan标准型在相似变换下的稳定群的结构 ,利用有限域上 2 -幂零矩阵构作了一个Cartesian认证码 ,计算出了该认证码的参数 .
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  “jordan标准”译为未确定词的双语例句
     Construction of Cartesian Authentication Codes from 2-Jordan Normal Form of Matrices
     由矩阵的2-Jordan标准型构造Cartesian认证码
短句来源
     This paper is devoted to the study of a nonhomogeneours nth order linear ordinary differential equations with constant coefficients P(D)x=acose t+bsine t Where P(D)=D n+a 1D n-1+. . .
     本文利用等价方程组 ,友矩阵与 Jordan标准型 ,研究了 n阶常系数线性非齐次常微分方程P(D) x=acoset+ bsinet其中 P(D) =Dn + a1Dn-1+… + an,D=ddt,a1,a2 ,… ,an,a,b为任意实常数 .
短句来源
     Finally, the application of Jordan Cononical matrix in proving Hamilton Cayley Theorem is introduced.
     本文最后还介绍了Jordan标准形在证明Hamilton—cayley定理中的应用.
短句来源
     And the methods which are based on the state transformation from systems ( A,B,C ),particularly all kinds of systems (Λ, B,C ) and systems (J,B,C) into the systems ( M,, ) are also proposed indirectly.
     且暗示出一种把系统(A,B,C),特别是无论特征值相同或相重与否,也无论同一个特征值组成多个Jordan块与否的对角型或Jordan标准型状态变换为模式系统(M,B~,C~的方法
短句来源
     A new construction of Cartesian authentication codes from the 2-Jordan normal form of matrices over finite fields is presented, and its size parameters are computed.
     利用有限域上矩阵的2-Jordan标准型构造了一类新的Cartesian认证码,计算了全部参数。
短句来源
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  jordan canonical
LetJ be the Jordan canonical matrix ofB andB=PJP-.
      
The author proves: There is a solution of (1) ? there are anmn×n matrixC, ann×n matrixQ and ann×n function matrixN such thatP*VC=QN, where detQ≠0 andN is defined byN(t=0)=En anddN/dt=RN, in whichR is ann×n Jordan canonical matrix.
      
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.
      
Jordan canonical forms of matrices over quaternion field
      
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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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