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- A real symmetric matrix A can be expressed as ??. 一个实对称矩阵A能被表示为??。
- A method of estimating the maximum and minimum eigenvalue of real symmetric matrices is given in this article, and its application is also discussed. 摘要本文给出了实对称矩阵最大与最小特徵值的一种估计方法及其应用。
- Davidson method and Newton method are two effective methods for computing the extreme eigenvalues of symmetric matrices. Davidson方法和Newton方法是求解对称矩阵特征值的两种有效方法。
- We extend Hua's fundamental theorems of the geometry of self-adjoint matrices and symmetric matrices to the infinite-dimensional case. 摘要本文分别将华氏自伴矩阵几何与对称矩阵几何基本定理推广到无限维的情形。
- Introduces the two-eigenvalue problem of a symmetric matrix and gives a formula to compute the matrix. 摘要介绍了对称矩阵的两特征值问题，并给出了计算公式。
- In this paper, we characterize the linear operators preserving adjoint matrices on the spaces of all matrices, symmetric matrices and upper triangular matrices over domain. 摘要木文刻画了整环上的全矩阵空间、对称矩阵空间和上三角矩阵空间上保持伴随矩阵的线性算子的结构。
- In the discussion of Euclid space ,the matter if n order real symmetric matrix A is positive definite remained important in the theory of matrix . 讨论Euclid空间中n阶实对称矩阵A是否正定,一直是矩阵理论中的重要问题。
- As for computing the largest eigenvalue and its eigenvector of a higher-order real symmetric matrix in the algorithm, the power method is used. 对于算法中涉及的求高阶实对称阵的最大特征值及其特征向量，采用幂法加以实现。
- By using the contain theory and partition theorem of symmetric matrix three conjectures about YANG Hui matrix are cetified. 它使用了对称矩阵特徵根的包含原理和分隔定理，并利用了正矩阵特徵根的性质。最后证实了关于杨辉矩阵的三个猜想。
- The preconditioning techniques for computing approximation of the large symmetric matrix are introduced, and improved algorithm and its convergence are presented. 首先引入求解大型对称特征值问题的预处理技术，给出了改善后的算法及相应的算法收敛分析。
- To solve this problem, two key inequalities are presented.The inequalities are used to improving the smoothed complexity of condition number of symmetric matrix. 然后将这两个不等式用于对称矩阵条件数的平滑分析,得到更简单、更低的平滑复杂度;
- With this algorithm，the number of eigenvalues of a real symmetric matrix in the given interval can be counted，and the eigenvalues of the matrix can be calculated. 该算法可求出实对称矩阵在给定区间内的特征值的个数，并可计算满足精度要求的特征值。
- An algorithm for solving linear equations, the paper shown strong Stability algorithms on the class of non-singular symmetric matrices and on the class symmetric positive definite matrices. 摘要关于线性方程解的算法方面，本文在对称非奇异矩阵类和对称正定矩阵类上给出了强稳定性算法。
- And then, they establish the global convergence theory of the algorithm when the system matrix of the linear complementarity problem is an H-matrix or a symmetric matrix. 当问题的系数矩阵为对角元为正的H-矩阵或对称半正定矩阵时，证明了算法的全局收敛性；
- In addition,we studied the relation between symmetric matrix and sub-involutory matrix,and the relation between symmetric matrix and sub-orthogonal matrix,which have been proved theoretically. 研究了次对称矩阵的性质,次对称矩阵与次对合矩阵,次正交矩阵的关系,并加以理论证明,得到了一些重要的结论。
- This paper presents a algorithm for distinguishing a real symmetric matrix into a positive definite, positive semidefinite, negative definite, negative semidefinite or non-definite matrix. 给出判别实对称矩阵为正定、半正定、负定、半负定或不定的一个算法；采用选最大对角元的方法，可使数值计算稳定性好。
- non-alternate symmetric matrices 非交错对称矩阵
- semi-definite symmetric matrices 对称半正定矩阵
- positive definite symmetric matrices 正定对称矩阵
- If a symmetrical matrix is positive definite, the determinants of all its minors are also positive. 如果对称矩阵是为正定者，它的所有子式的行列式也都是正的。
