[數] 正定矩陣
Results linear complementary problem have unique solution when M is generalized positive definite matrix.
結果得到了當M是廣義正定矩陣時，線性互補問題存在唯一解。
General solutions of above inverse problem in positive definite matrix and in orthogonal matrix are given here by using factorization method of matrix.
本文用矩陣分解法給出該反問題在正定矩陣類及正交矩陣類中的通解。
In this paper, we discuss properties of positive definite complex matrix, and the relation between it and the Hermite positive definite matrix.
本文給出了全正定矩陣的概念，讨論了全對稱實矩陣是全正定矩陣的幾個充分必要條件。
A unified ****** condition for stable matrix, positive definite matrix and M matrix is presented in this paper.
本文給出了一個判定矩陣穩定、正定以及為M矩陣的統一簡化條件。
When a common positive definite matrix can not be found to design fuzzy model-based controller, the improved adaptive reconfigurable control scheme based on fuzzy model and neural network is proposed.
同時，當現有的基于模型的模糊控制器無法求解時，文中給出了一種改進的基于模糊模型和神經網絡的自適應重構控制方案。
This paper presents a sufficient and necessary conditions for generalized positive definite matrix, its relation with complete main positive matrix.
本文給出廣義正定陣判别方法，讨論幾類矩陣之間的關系；
To In this paper, the definition of complex generalized positive definite matrix is given, its fundamental properties are stu***d, and its equivalent characteristics are established.
當引入廣義正定複矩陣這個概念之後，也應該讨論它相應的性質與結構，這對豐富矩陣論的内容無疑是有意義的。
Based on the definitions of generalized positive definite matrix, a further study of it is made in the present paper, and several new results are obtained as a consequence.
提出了超正穩定的概念，讨論了實對稱正定、亞正定、良廣義正定、廣義正定、超正穩定及正穩定矩陣類之間的關系，得到了若幹确定的結果。
And then the eigenvalue problem of integral equation is transformed into the standard eigenvalue problem of a positive definite matrix with infinite order.
進而将積分方程形式的特征值問題轉化為無窮階正定對稱矩陣的标準特征值問題。
It wishes to find a new way for normative research into the concept of generalized positive definite matrix .
希望為廣義正定矩陣概念的規範化探出一條新路。
Sub-positive definite matrix class and real-normal matrix class are made further development to a new class of matrix—Sub-normal matrix.
對亞正定矩陣類與實規範矩陣類作進一步拓廣，得到一個新的矩陣類——亞規範矩陣。
In this paper, some important inequalities on norm of determinent of complex positive definite matrix and its Schur complement are obtained.
正定複矩陣是矩陣論中的一個重要概念，人們已經掌握了它的若幹性質與結構。
Aim To solve question about the existence and uniqueness of the solution for linear complementary by using generalized positive definite matrix.
本文主要研究非線性互補問題，提出了一個求解非線性互補問題的微分方程方法并進行了相應的數值實現。
In this paper, we have given several properties of determinant and trace for positive definite complex matrix, and improves some existing results.
本文繪出了複正定矩陣的迹和行列式的幾個性質，改進了現有的一些結果。
As one of its application, we prove a number of important inequalities of the determinantal modulus of a positive definite complex matrix.
作為它的應用之一，本文推得正定複矩陣的行列式的模的一些重要不等式。
Based on the eigensubspace estimation using discrete recurrent neural networks, we propose algorithms to solve the problem of eigensubspace estimation for positive definite symmetric matrix.
基于運用回複式離散神經網絡進行特征子空間估值的理論，提出了解決正定對稱矩陣的特征子空間估值問題的算法。
A method for getting the values of the unknown parameters of the semiparametric model is given under the principle of penalized least squares with a positive definite regular matrix.
利用補償最小二乘原理構造加權懲罰平方和，得到半參數模型中正規化矩陣正定時參數和半參數的估計量。
Using the determinant and trace of positive definite Hermite matrix of complex fields we obtained several interesting inequalities.
本文考慮了複數域上正定厄米特矩陣的行列式與迹間的一類不等式，得到了幾個有趣的不等式。
In this paper, we give a general spectral resolution of real matrix and some properties eigenvalue of a general positive definite real matrix.
給出實矩陣的廣義譜分解式，讨論廣義正定實矩陣的特征根的一些性質。
The method ICCG. is one of the best iterative method for solving the system of linear algebraic equations, but it can only be applied to the symmetric and positive definite coefficient matrix.
ICCG方法是解線性代數方程組較為理想的方法，但它僅適用于具有正定對稱的系數陣。
In this paper, two inequalities of the positive semi-definite matrix trace are given.
本文讨論譜約束下實對稱半正定矩陣束的最佳逼近問題，指出一般算法。
The paper gives a number of methods for differentiating half positive definite quadratic form and some relevant properties in respect to half positive definite corresponding coefficient matrix.
本文給出的半正定二次型的若幹判别方法及半正定對應系數矩陣的一些相關性質。
A ****** proof of positive semi-definite of Gram matrix is given, and several important conclusions of Gram determinant are discussed in this paper.
本文給出格拉姆矩陣的半正定性的簡單證明，讨論格拉姆行列式的幾個重要結論，并應用于一類不等式的證明。
Some equivalent representations of complex positive semi definite matrices are given by using equivalent conditions of positive semi definite of real symmetric matrix.
利用實對稱矩陣的半正定之等價條件給出了複正半定矩陣的幾個等價條件。
正定矩陣（positive definite matrix）是線性代數中的重要概念，具有以下核心特征和應用：
對于實對稱矩陣 ( A in mathbb{R}^{n times n} )，若對任意非零向量 ( mathbf{x} in mathbb{R}^n )，滿足： $$ mathbf{x}^T A mathbf{x} > 0 $$ 則稱 ( A ) 為正定矩陣。若條件改為 ( geq 0 )，則為半正定矩陣。
矩陣 ( A = begin{pmatrix} 2 & -1-1 & 2 end{pmatrix} ) 是正定的，因為：
正定矩陣是一種特殊類型的矩陣，其所有特征值均為正數，具有許多重要的應用。以下是對正定矩陣的詳細解釋：
正定矩陣在數學和工程學中都有廣泛應用，例如：
正定矩陣的定義是：如果對于任意非零向量x，都有x^T Ax>，那麼矩陣A就是正定的。其中，x^T是x的轉置，^T表示轉置操作。
正定矩陣具有以下特點：
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