广义对称自正交相似矩阵反问题的最小二乘解

Least-squares Solution for Inverse Problem of Generalized Symmetric and Self-orthogonal Similar Matrix

J是反对称正交矩阵,A∈R2k×2k,如果JAJT=AT,AT=A,则称A为广义对称自正交相似矩阵,全体n阶广义对称自正交相似矩阵的集合记为GSRn×n,n=2k。研究了2个广义对称自正交相似矩阵反问题,给出了问题Ⅰ解的通式及问题Ⅱ唯一解的表达式。

J is a anti-symmetric and orthogonal matrix, A∈R^2k×2k,if JAJ^T=A^T,A^T=A,then A is generalizedsymmetric and self-orthogonal similar matrix. Discussing the two problems, the existence of the solution for Problem Ⅰ and uniqueness of the solution for Problem Ⅱ are proved . The general form of Sr is given and the expression of A is presented.