矩阵方程AX=B的谱范数约束解  

Constrained Solutions of the Matrix Equation AX=B in the Spectral norm

作　　者：刘喜富 罗乐 LIU Xifu;LUO Le(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《四川师范大学学报（自然科学版）》2023年第1期58-65,共8页Journal of Sichuan Normal University（Natural Science）

基　　金：重庆市科委面上项目(cstc2021jcyj-msxmX0195)。

摘　　要：奇异值分解是求解约束矩阵方程的有效手段.首先根据奇异值分解得到矩阵方程解的分块表达式,再利用分块矩阵的保范扩张定理,得到相容矩阵方程AX=B在谱范数约束下的一般解、Hermitian解和半正定解.Singular value decomposition is a useful method to solve the constrained matrix equation. Firstly, we obtain the expressions of the solutions by using singular value decomposition. Secondly, applying theorems of the norm-preserving dilation for bolck matrices, we establish the representations for the general solution, Hermitian solution and positive semidefinite solution of the consistent matrix equation AX=B with the spectral norm constraints.

关 键 词：矩阵方程 奇异值分解 约束解 谱范数 

分 类 号：O151.2[理学—数学]