The conditions of positive semidefinite quadratic form are given according to its definition,and some properties of postive semidefinite matrix are given according to its definition in the paper.
从半正定二次型的定义出发 ,推导出与其定义等价的几个条件 ;并且根据半正定矩阵的定义 ,推导出半正定矩阵的若干性
The complex matrix solutions with Hermite part positive semidefinite and Hermite positive semidefinite for the matrix equation(A*XA,B*XB)=(C,D) is investigated.
研究了复矩阵方程(A*XA,B*XB)=(C,D)有Hermite部分是半正定的解与Hermite半正定解的可解性条件。
This paper investigates the constraned singular semi-positive definite linear systems Ax=b,(x∈L).
本文研究约束的奇异半正定线性方程组Ax=b,x∈L的迭代解法,给出了著名的Ke ller定理的新证,并据之给出了已有的投影迭代法的简证。
Using Toeplitz matrix,the feature that the sum of the length of two sides is larger than that of the other side and the linearity transformation, the positive semi-definite sextic polynomial are derived, that is,L m(m=1,2,3,4,5),M n,B n(n=1,2,3,4) and the concrete expressions of G 1,G 2.
应用Toeplitz矩阵、三角形两边之和大于第三边的性质与线性交换 (x ,y ,z) =(a ,b ,c)θ(0 ) ,给出了半正定三元六次型Lm(m =1,2 ,3,4 ,5 ) ,Mn,Bn(n =1,2 ,3,4 )和G1,G2 的具体表达式 ,然后给出主要结果Lm,Mn,G1,G2 ,B1,B2 及B3 +B4∈Q(A) 。
The author introduce the method of applying positive semi-definite quadratic form to prove inequality by giving several examples.
通过给出几个实例 ,介绍了利用二次型的半正定性证明不等式的方法 。
A sufficient and necassary condition and the general form of solutions for the inverse problem of the system of quaternion linear equations Ax=b to have solutions of positive semi-definite matrix and positive semi-definite conjugate matrix are derived.
证得了四元数矩阵为半正定的充要条件，得到四元数线性方程组ＡＸ＝ｂ的反问题有半正定阵解、半正定自共轭阵解的充要条件及解的一般形式。
The Equal Condition of Semipositive Subdefinite Matrix and Left and Right Inverse;
亚半正定阵的判别及左右逆特征值问题
On the Matrix Inequalitiy for the Hadamard Product of Positive Semidefinite Matrices
关于半正定矩阵Hadamard积的矩阵不等式
Connections Between Euclidian Distance Matrix and Positive Semidefinite Matrix
欧几里得距离矩阵与半正定矩阵的关系
On the Metapositive (Semi) Definite Solutions of Linear Equation AXB=C;
矩阵方程AXB=C的亚(半)正定解
The Bisymmetric Positive Semidefinite Solutions of Matrix Equation A~TXA=F;
矩阵方程A~TXA=F的双对称半正定解
An Inequality For Semipositive Definite Hermite s Matrices;
半正定Hermite矩阵的一个不等式
Symmetric Semipositive Definite Solutions to Matrix Equation AXA~т+BYB~т=C;
矩阵方程AXA~T+BYB~T=C的对称半正定解
The Trace of A Positive Semidefinite Hermite Matrix and Its Application;
半正定Hermite矩阵的迹及其应用
The Isolation of Generalized Minkowski′s Inequality for Semi-metapositive Definite Matrix
亚半正定矩阵的广义Minkowski不等式的隔离
Estimates for Elgenvalues of Product of Positive Semidefinite Hermitian Matrices
半正定Hermite矩阵之积的特征值估计
The Positive Semi-definite of Gram Matrix and it's Application
格拉姆(Gram)矩阵的半正定性及其应用
On Partial Ordering of Pseudo-Schur Complement for Positive Semidefinite Block Matrices
半正定分块矩阵的块Pseudo-Schur补的偏序
Positive semi-definite matrices are positive definite if and only if they are nonsingular.
正半定矩阵是正定的，当且仅当它们是非奇异矩阵。
An Approximation Method of Positive Semi-definite Matrix Based on Weighted F-norm;
一种基于加权F-范数的半正定矩阵的逼近方法
An Inequality for the Eigenvalue of the Product of Positive Semedefinite Hermitean Matrices;
一个关于半正定Hermite矩阵特征值的不等式
Minor Self-conjugate and Skewpositiove Semidefinite Solutions to a Matrix Equation over Skew Fields;
体上一矩阵方程的次自共轭及斜亚半正定解
Determinantal Inequality of Sum of Positire Semidefinite Self-conjugate Quaternion Matrices;
半正定自共轭四元数矩阵之和的行列式不等式
Least-Square Solutions of Inverse Problems for Positive Semidefinite and Bisymmetric Matrices;
一类半正定双对称矩阵反问题的最小二乘解