positive semidefinite matrix meaning in English
半正定矩阵
非负半正定阵
Examples
- The eigenvalues of positive semidefinite matrices
半正定矩阵乘积的特征值 - The left and right inverse eigenvalue problem for symmetric positive definite and symmetric positive semidefinite matrices on subspace
子空间上的对称正定及对称半正定阵的左右特征值反问题 - In the first part , we shall prove several inequalities involving symmetric positive semidefinite , general m - matrices and inverse m - matrice which are generalization of the classical oppenheim ' s inequality for symmetric positive semidefinite matrices
第一个部分给出了半正定矩阵，一般的m -矩阵以及逆m -矩阵的一些相关不等式，而这些不等式都是有关半正定矩阵的经典的oppenheim不等式的推广。 - The second part of this paper is mainly concerned about an interesting matrix inequality presented in [ 5 ] , which is then generalized in m ~ " under the entry - wise nonnegative ordering . we introduced the concept of sub - kronecker product , and establish an inequality which relates the schur complement of a and b for positive semidefinite matrices a and b . our results improve the related known results obtained by t . l . markham and r . l . smith in 1998 ( see [ 5 ] )
第二部分研究了文献[ 5 ]中提出的一个有趣的矩阵不等式，并将此不等式在逆m -矩阵中推广，然后引入次kronecker乘法的概念，提出并证明了一个更广泛的不等式，改进了t . l . markham和r . l . smith在[ 5 ]中的有关结果。 - 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。