positive matrices 中文意思是什麼
positive matrices
解釋
正矩陣-
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。 -
On dx - generalized positive definite matrices
廣義正定矩陣 -
Negative matrices over a c - algebra and geometric mean of two positive definite elements
代數上的非負矩陣與正定元的幾何平均 -
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。 -
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
第一個部分給出了半正定矩陣，一般的m -矩陣以及逆m -矩陣的一些相關不等式，而這些不等式都是有關半正定矩陣的經典的oppenheim不等式的推廣。 -
A new method on the decision of positive definite quadratic form using the real square matrices
利用實方陣判定二次型正定性的新方法 -
On the positive definiteness of the product of matrices
乘積的不等式的討論 -
In mmse based detection algorithms it ’ s inevitable to do the matrix inversion operation, and we have found by analysis that such matrices are all positive definition hermite matrices. so, in chapter three, by renumbers the looped variables we induce a new matrix inversion algorithm and based on the symmetry of the data we further
由於基於mmse的檢測演算法中會不可避免地遇到矩陣求逆運算，經過分析發現此類矩陣均為正定hermite矩陣，根據此類矩陣的特點引入了變量循環重新編號法求逆演算法，並且根據運算過程中數據的對稱性提出了進一步的簡化方案。 -
Necessary and sufficient conditions for two positive stable matrices
論正規矩陣的充要條件 -
Positive semi-definite matrices are positive definite if and only if they are nonsingular.
正半定矩陣是正定的，當且僅當它們是非奇異矩陣。 -
Completely positive matrices having cyclic graphs
圖是圈的完全正矩陣 -
We extend the determinant inequality of generalized real positive definite matrices that is advanced by paper [ 3 ]. moreover we give its convex inequality
摘要推廣了文獻[ 3 ]中的廣義實正定矩陣的行列式不等式，同時給出了廣義實正定矩陣的凸性不等式。 -
Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices
主要內容有：行列式，矩陣的代數運算，維向量空間的概念，線性方程組理論，矩陣相似的標準形理論，二次型等。 -
Based on the results, chapter 3 obtains the necessary and sufficient conditions of the positive line a - doubly diagonally dominant matrices being non - singular m - matrices, by means of the nature of the associated digraph of matrices irreducible and weakly irreducible matrices. the results obtained simplify the process of judgment, only making us to check the related quantity involved in the circuit of the associate digraph of matrices
第三章在已有結果的基礎上，藉助于矩陣的伴隨有向圖、不可約以及弱不可約矩陣的性質，得到了正線-雙對角占優矩陣為非奇異m -矩陣的充分必要條件，所獲結果簡化了判定過程，只需要對矩陣伴隨有向圖圈中所涉及到的相關量進行驗證即可。 -
Perturbation analysis on symmetric indefinite and generalized semi - positive matrices
關于對稱不定和廣義半正定矩陣的擾動分析 -
Although there have been some suggestions on how to ensure the positive definiteness of the iterative matrices, they are restrictive and is not easy to be implemented
盡管已有一些關于怎樣保證迭代矩陣正定的討論，然而還沒有切實可行的方案。 -
Finally, when the decomposition is proceeding to a symmetric positive definite matrix, the pivot may be very small or even negative. there provided several methods to overcome this shortcoming. ( 2 ) for the block strictly diagonally dominant matrices, there proved the existence and uniqueness of the block lu decomposition and the existence of the incomplete version
（ 2 ）證明了嚴格塊對角占優矩陣塊lu分解的存在唯一性與塊不完全lu分解的存在性，以及嚴格塊對角占優矩陣與不可約塊對角占優矩陣的塊jacobi 、塊gs ，塊sor 、塊ssor等基本迭代法的收斂性。 -
A survey on completely positive matrices
有關完全正定陣的綜述 -
The related results of the definite positive matrices are extended
推廣了關於半正定矩陣的相應結果。 -
The relation between some special matrices and its squares are discussed, in the sense of the star partial ordering, the minus partial ordering and lower partial ordering, the related results of the definite positive matrices are extended, some related results on the general matrices are obtained
研究矩陣及其平方矩陣偏序之間的關系，解決了j . k . baksalary和f . pukesheim提出的公開問題，並推廣到更一般的情形，對於一般矩陣同時得到了若干新結果，推廣了關于（半）正定矩陣的相應結果。
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