# 双对称 meaning in English

###### Translation Mobile
• disymmetry
◇双对称面 disymmetric face; 双对称色散 disymmetric dispersion
###### Examples
• One kind of inverse problem for the bisymmetric matrices
双对称矩阵的一类反问题
• Bisymmetric nonnegative definite solution of matrix equations atx
双对称非负定解
• Inverse problem for general bisymmetric matrices
广义双对称矩阵反问题
• Least square solutions of matrix equation axb
范数双对称
• The generalized bisymmetric solution and generalized anti - bisymmetric solution of
的广义双对称解与广义双反对称解
• D . x . xie , l . zhang and x . y . hu , least - square solutions of inverse eigenvalue probem of bisymmetric matrices , math . numer sinica , 1 ( 1999 ) 62 - 72
廖安平,谢冬秀,双对称非负定矩阵一类逆特征值问题的最小二乘解,计算数学, 23 : 2 ( 2001 ) 209 - 218
• This ph . d . thesis - firstly considers the real asymmetric , real symmetric , bisym - metric , and symmetric and skew antisymmetric matrix extension problems constrained by the matrix inverse problem ax = b . and also considers , in the solution set , of the corresponding matrix extension problems , the optimal approximation solution to a given matrix a * . the necessary and sufficient conditions for the existence of and the expressions for the above problems are derived , and the numerical algorithm and examples to solve the problems are also given
首次提出并讨论了矩阵反问题ax = b约束下实矩阵、实对称矩阵、双对称矩阵和对称次反对称矩阵的扩充问题，讨论了在其解集合中与给定矩阵a ~ *的最佳逼近问题，得到了问题的解存在的条件及通式的表示，给出求解问题的数值算法和数值例子。
• In this thesis , we study some open problems and conjectures about the linear complementarity problem . it consists of the next three aspects : firstly , we study murthys " open problem whether the augmented matrix is a q0 - matrix for an arbitary square matrix a , provide an affirmable answer to this problem , obtain the augmented matrix of a sufficient matrix is a sufficient matrix and prove the graves algorithm can be used to solve linear complementarity problem with bisymmetry po - matrices ; secondly , we study murthys " conjecture about positive semidefinite matrices and provide some sufficient conditions such that a matrix is a positive semidefinite matrix , we also study pang ' s conjecture , obtain two conditions when r0 - matrices and q - matrices are equivelent and some properties about e0 q - matrices ; lastly , we give a counterexample to prove danao ' s conjecture that if a is a po - matrix , a e " a p1 * is false , point out some mistakes of murthys in [ 20 ] , obtain when n = 2 or 3 , a e " a p1 * , i . e . the condition of theorem 3 . 2 of [ 25 ] that a p0 can be deleted and obtain a e " a is an almost e - matrix if a is a co - matrix or column sufficient matrix
本文分为三个部分，主要研究了线性互补问题的几个相关的公开问题以及猜想： ( 1 )研究了murthy等在[ 2 ]中提出的公开问题，即对任意的矩阵a ，其扩充矩阵是否为q _ 0 -矩阵，给出了肯定的回答，得到充分矩阵的扩充矩阵是充分矩阵，并讨论了graves算法，证明了若a是双对称的p _ 0 -矩阵时， lcp ( q ， a )可由graves算法给出； ( 2 )研究了murthy等在[ 6 ]中提出关于半正定矩阵的猜想，给出了半正定矩阵的一些充分条件，并研究了pang ~ -猜想，得到了只r _ 0 -矩阵与q -矩阵的二个等价条件，以及e _ 0 q -矩阵的一些性质； ( 3 )研究了danao在[ 25 ]中提出的danao猜想，即，若a为p _ 0 -矩阵，则，我们给出了反例证明了此猜想当n 4时不成立，指出了murthy等在[ 20 ]中的一些错误，得到n = 2 ， 3时，即[ 25 ]中定理3 . 2中a p _ 0的条件可以去掉。
• Based on the properties of bisymmetric matrices , a class of constrained inverse eigenproblem and associated approximation problem for bisymmetric matrices were essentially decomposed into the same kind of subproblems for real symmetric matrices with smaller dimensions , and the solutions of the two problems were obtained by applying the conclusions of real symmetric matrices
摘要根据双对称矩阵的性质，将双对称矩阵的一类约束逆特征值问题及其逼近问题分解成具有较小阶数的实对称矩阵的同类子问题，然后利用实对称矩阵的结果导出双对称矩阵的这两个问题的解。
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