positive semidefinite matrix 中文意思是什麼

positive semidefinite matrix 解釋
半正定矩陣
  • positive : adj 1 確實的，明確的；確定的；無條件的 （opp qualified implied inferential）; 絕對的，無疑問的，...
  • semidefinite : 半定的
  • matrix : n （pl matrices 或matrixes）1 【解剖學】子宮；母體；發源地，策源地，搖籃；【生物學】襯質細胞；間...
  1. 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

    本文分為三個部分，主要研究了線性互補問題的幾個相關的公開問題以及猜想： （ 1 ）研究了murthy等在[ 2 ]中提出的公開問題，即對任意的矩陣a ，其擴充矩陣是否為q _ 0 -矩陣，給出了肯定的回答，得到充分矩陣的擴充矩陣是充分矩陣，並討論了graves演算法，證明了若a是雙對稱的p _ 0 -矩陣時， lcp （ q ， a ）可由graves演算法給出； （ 2 ）研究了murthy等在[ 6 ]中提出關於半正定矩陣的猜想，給出了半正定矩陣的一些充分條件，並研究了pang ~ -猜想，得到了只r _ 0 -矩陣與q -矩陣的二個等價條件，以及e _ 0 q -矩陣的一些性質； （ 3 ）研究了danao在[ 25 ]中提出的danao猜想，即，若a為p _ 0 -矩陣，則，我們給出了反例證明了此猜想當n 4時不成立，指出了murthy等在[ 20 ]中的一些錯誤，得到n = 2 ， 3時，即[ 25 ]中定理3 . 2中a p _ 0的條件可以去掉。
  2. 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 ] )

    第二部分研究了文獻[ 5 ]中提出的一個有趣的矩陣不等式，並將此不等式在逆m -矩陣中推廣，然後引入次kronecker乘法的概念，提出並證明了一個更廣泛的不等式，改進了t . l . markham和r . l . smith在[ 5 ]中的有關結果。
  3. The semidefinite positive on the tensor product of matrix

    矩陣張量積的半正定性
  4. Positive semidefinite hermitian matrix solution of a matrix equations

    特殊子空間上矩陣方程有解的判定
  5. The results of this paper extend the existed results of normal systems to descriptor systems. 8. lower and upper matrix bounds for the positive semidefinite solution of discrete - time riccati matrix equation are obtained

    給出離散ricoati方程和統一的耦合代數ricoati方程的半正定解的上、下矩陣邊界估計，並得到求離散ricoat方程和統一的耦合代數ricoati方程的半正定解的兩個迭代演算法。
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