乘积矩阵的奇异值估计

Estimation of Singular Values for Product Matrices

本文给出了m 个矩阵乘积的奇异值估计:m ax∑mj= 1i(j)= (m- 1)n+ i∏mj= 1σ(j)i(j) ≤σi ≤ m in∑mj= 1i(j)= i+ m - 1∏mj= 1σ(j)i(j), 1 ≤i≤n同时给出了∑ki= 1 σi,∏ki= 1 σi

In this paper,the authors give the estimation of singular values for product of m matrices: max ∑mj=1i (j) =(m-1)n+i ∏mj=1σ (j) i (j) ≤σ i≤ min ∑mj=1i\+\{(j)\}=i+m-1 ∏mj=1σ (j) i (j) , 1≤i≤nand give a lower bound of ∑kj=1σ\-i and ∏ki=1σ\-i as well.