In mathematics, matrix is an array of numbers enclosed in brackets. When these numbers are complex in nature, the matrices are called the complex matrices. Complex matrices may be divided into different types with Hermitian matrix being one of them....
It is a classical result of Ginibre that the normalized bulk $k$-pointcorrelation functions of a complex $nimes n$ Gaussian matrix with independententries ... T Tao,V Vu - 《Communications in Mathematical Physics》 被引量: 134发表: 2012年 On Conjugate Gradient type methods and polynomial prec...
When these two matrix equations are consistent, the convergence theorem shows that a solution can be obtained within finite iterative steps in the absence of round-off error for any initial arbitrary Hermitian R R mathContainer Loading Mathjax -conjugate solution matrices V 1 V 1 mathContainer ...
Let P∈C^( m×m )and Q∈C^( n×n) be Hermitian and{k+1}-potent matrices,i.e.,P k+1=P=P,Qk+1=Q=Q,where(·)stands for the conjugate transpose of a matrix.A m... 董昌州,李浩雪 - 《数学季刊(英文版)》 被引量: 0发表: 2023年 加载更多来源...
It is known that solving coupled matrix equations with complex matrices can be very difficult and it is sufficiently complicated. In this work, we propose two iterative algorithms based on the Conjugate Gradient method (CG) for finding the reflexive and Hermitian reflexive solutions of the coupled ...
The iterative method of the generalized coupled Sylvester-conjugate matrix equations over Hermitian and generalized skew Hamiltonian solution is presented. When these systems of matrix equations are consistent, for arbitrary initial Hermitian and generalized skew Hamiltonian matrices X (j) (1), j = 1,...
By proper formulation of a step in the factorization algorithm of an elementary paraconjugate Hermitian polynomial matrix the exponential time-bound can be reduced to low polynomial one. As the remaining steps have polynomial time-bound a big save is expected in larger problems. The reduction is ...
(2) where all time-varying matrices are in ℍ𝑛×𝑛, ()∗ denotes the conjugate transpose, and 𝐵˜(𝑡) and 𝐶˜(𝑡) are assumed to be positive semidefinite (i.e., 𝐵˜(𝑡)=𝐵˜∗(𝑡)≥0 and 𝐶˜(𝑡)=𝐶˜∗(𝑡)≥0). According to [15...