查询词典 bisymmetric

Necessary and sufficient conditions for the existence and the expressions of selfconjugate solution, perselfconjugate solution, centrosymmetric solution, bisymmetric solution, skewselfconjugate solution, skewperselfconjugate solution, skewcentrosymmetric solution, and skewbisymmetric solution to 4 kinds of systems of linear matrix equations over a regular ring with an involutorial antiautomorphism are given.

利用矩阵技巧和所建立的矩阵理论，给出了正则环上五类矩阵方程组有解的若干充要条件和一般解的表达公式。这些矩阵方程组除了它们在理论上有重要的意义外，还有重要的应用价值。在具有对合反自同构的正则环上，给出了四类矩阵方程组有双对称解，中心对称解，斜中心对称解，广自共轭解，斜广自共轭解，自共轭解以及斜自共轭解的充要条件及其这些解的具体表达式。

Exive least-squares solutions, antire?exive least-squares solutions, bisymmetric least-squaressolutions, symmetric and antipersymmetric least-squares solutions, symmetric or-thogonal symmetric least-squares solutions, symmetric orthogonal antisymmetricleast-squares solutions and their optimal approximation to the linear matrix equa-tion AX = B, and solve them successfully. 2. For Problem II, we can convert it to another problem of finding the least-squares solutions with the least norm of a new consistent matrix equation. Onthe base of the solutions of Problem I we can apply the iterative method to get

本文所构造的迭代法的优点在于先利用法方程变换将求矩阵方程的最小二乘解转化为求一个相容矩阵方程的解的问题，再利用迭代法对于任意给定的初始矩阵进行迭代，均可在有限步内迭代出所求问题的一个解；可将问题II转化为求新方程的极小范数解的问题，同样用迭代法求解，从而系统且全面地解决了问题I、II在约束矩阵类如中心对称、中心反对称、自反矩阵、反自反矩阵、双对称、对称次反对称、对称正交对称、对称正交反对称矩阵中的最小二乘解及其最佳逼近问题。

The stiffness matrix and geometric stiffness matrix of rectangular tube-in-tube element of which the cross-section has bisymmetric axes are developed.

导出了截面含双对称轴的矩形筒中筒单元刚度矩阵和单元几何刚度矩阵。

Finally, least-squares solution for the inverse problem of bisymmetric matrices with a submatrix constraint is proposed.

研究了子阵约束下双对称矩阵反问题的最小二乘问题。

The solution group such as symmetric, skew-symmetric, centrosymmetric, centroskew symmetric, reflexive, antireflexive, bisymmetric or symmetric and antipersymmetric are successfully found.

构造了一种迭代法系统地研究了问题Ⅴ的一般解组、对称解组、中心对称解组、自反矩阵解组、双对称解组、对称次反对称解组及其最佳逼近等问题，并成功地解决了这些问题。

Least-squares solution for the inverse problem of real matrices、symmetric matrices and bisymmetric matrices are studied in this thesis. The thesis includes the following contents.

本文研究了子阵约束下实矩阵、实对称矩阵和双对称矩阵反问题的最小二乘解，全文主要包括以下内容。

In this paper, we first introduce the concepts and structures of generalized per-symmetric matrix, generalized centro-symmetric matrix or generalized bisymmetric matrix.

本文介绍了广义广对称矩阵、广义中心对称矩阵以及广义双对称矩阵的概念及结构，研究了这些特殊矩阵集合中，矩阵方程AXB=C及矩阵方程组A_1XB_1=C_1，A_2XB_2=C_2的迭代解法，同时考虑了相应的最佳逼近问题。

For fixed generalized reflection matrix P, i.e., P^T=P, P^2=I, then matrix X is said to be generalized bisymmetric, if $X=PXP$ and $X=X^T$.

对于某个广义反射阵P，满足P^T=P， P^2=I，那么称矩阵X是广义双对称的，如果满足X=PXP及X=X^T。

In this paper, an iterative method is established to solve the linear matrix equation $AXB=C$ over generalized bisymmetric $X$.

本文给出了求解矩阵方程AXB=C广义双对称解的迭代解法。

Iterative method; Generalized bisymmetric solution; Least-norm solution; Optimal approximation

迭代解法；广义双对称解；极小范数解；最佳逼近。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失