可非负扩张块Hankel矩阵的因子分解

FACTORIZATION OF NONNEGATIVELY EXTENDABLE BLOCK HANKEL MATRICES

利用作者和陈公宁教授已经获得的结果 ,证明每个可非负扩张的块Hankel矩阵Hn ,p=(Si+j) ni,j=0 ,Sk=S k ∈Cp×p总可以分解成为一个广义的Vandermonde矩阵Vg,一个对角矩阵D以及Vg 的共轭转置V g 的乘积形式 ,这里去掉了Tismenetsky相应的分解形式中对Hn ,p非奇异性的限制 .

Based on the use of the results established by Chen Gongning and Hu Yongjian, it is proved that each nonnegatively extendable block Hankel matrix H n,p =(S i+j ) n i,j=0 , S k=S * k∈C p×p can be partitioned into a product of a generalized Vandermonde matrix V g, a diagonal matrix D and the conjugate transpose of V g, and therefore, the nonsingularity constraint of H n,p in the associated factorization results of Tismenetsky may be omitted.