共查询到18条相似文献,搜索用时 62 毫秒
1.
袁晖坪 《数学的实践与认识》2006,36(11):202-206
两复正定矩阵之和必是复正定矩阵,但其积未必是复正定矩阵.研究了复矩阵之积的正定性,给出了复矩阵之积为复正定矩阵的一系列判定条件,获得了一些新的结果,改进并推广了K y Fan T aussky定理及Fe jer定理. 相似文献
2.
3.
郑建青 《纯粹数学与应用数学》2014,(1):45-52
利用复矩阵的Schur补和次正定性,研究了次正定复矩阵的次Schur补的一些性质,得到了次正定复矩阵次Schur补的几个行列式不等式,将相关文献的相应结果由次正定次Hermite矩阵推广到次正定复矩阵. 相似文献
4.
5.
6.
研究正定矩阵的子矩阵,利用合同标准形分别给出了复正定矩阵的子式阵为复正定矩阵和实正定矩阵的子式阵为实正定矩阵的充分必要条件,其结果简单而实用. 相似文献
7.
8.
9.
10.
关于复正定矩阵行列式的不等式 总被引:1,自引:1,他引:0
金能 《数学的实践与认识》2000,30(4)
本文讨论了复正定矩阵行列式的估计式 ,修正了文 [2 ]的一些错误 ,得到了一些复正定矩阵行列式的不等式 . 相似文献
11.
关于复正定矩阵的判定 总被引:5,自引:0,他引:5
袁晖坪 《数学的实践与认识》2004,34(2):133-138
研究了复矩阵的正定性 ,给出了复正定矩阵的一系列判定条件 ,获得了一些新的结果 ,改进并推广了著名的 Hadam ard不等式、Fejer定理及郭忠的结果 ,削弱了华罗庚不等式的条件 . 相似文献
12.
考虑非线性矩阵方程X-A*X-1A=Q,其中A是n阶复矩阵,Q是n阶Hermite正定解,A*是矩阵A的共轭转置.本文证明了此方程存在唯一的正定解,并推导出此正定解的扰动边界和条件数的显式表达式.以上结果用数值例子加以说明. 相似文献
13.
We derive a set of differential inequalities for positive definite functions based on previous results derived for positive definite kernels by purely algebraic methods. Our main results show that the global behavior of a smooth positive definite function is, to a large extent, determined solely by the sequence of even-order derivatives at the origin: if a single one of these vanishes then the function is constant; if they are all non-zero and satisfy a natural growth condition, the function is real-analytic and consequently extends holomorphically to a maximal horizontal strip of the complex plane. 相似文献
14.
KY Fan 《Linear and Multilinear Algebra》1973,1(1):1-4
Inequalities concerning real square matrices A with positive definite symmetric component A+A*are derived from certain inertia relations which hold for any complex (not necessarily real) square matrices A with positive definite
A+A* 相似文献
A+A* 相似文献
15.
In this paper we develop an appropriate theory of positive definite functions on the complex plane from first principles and show some consequences of positive definiteness for meromorphic functions. 相似文献
16.
17.
The well-known Lyapunov's theorem in matrix theory / continuous dynamical systems asserts that a (complex) square matrix A is positive stable (i.e., all eigenvalues lie in the open right-half plane) if and only if there exists a positive definite matrix X such that AX+XA* is positive definite. In this paper, we prove a complementarity form of this theorem: A is positive stable if and only if for any Hermitian matrix Q, there exists a positive semidefinite matrix X such that AX+XA*+Q is positive semidefinite and X[AX+XA*+Q]=0. By considering cone complementarity problems corresponding to linear transformations of the form I−S, we show that a (complex) matrix A has all eigenvalues in the open unit disk of the complex plane if and only if for every Hermitian matrix Q, there exists a positive semidefinite matrix X such that X−AXA*+Q is positive semidefinite and X[X−AXA*+Q]=0. By specializing Q (to −I), we deduce the well known Stein's theorem in discrete linear dynamical systems: A has all eigenvalues in the open unit disk if and only if there exists a positive definite matrix X such that X−AXA* is positive definite. 相似文献
18.
詹仕林 《数学的实践与认识》2003,33(9):123-125
本文指出文 [1 ]中的错误 ,并把文 [1 ]中关于复正定矩阵与正定 Hermite矩阵的行列式不等式推广到较为广泛的复矩阵类 相似文献