线性约束下反Hermitian广义反Hamiltonian矩阵的最佳逼近问题

The Optimal Approximation Problem of Anti-Hermitian Generalized Anti-Hamiltonian Matrices Under the Linear Constraint

讨论了线性约束下反Hermitian广义反Hamiltonian矩阵的最佳逼近问题。提出并征明了约束矩阵集合SA非空的充分必要条件,给出了集合SA中元素的一般表达式。对于任意一个复矩阵,得到了它在SA中的最佳逼近矩阵A的表达式。

The optimal approximation problem of anti-Hermitian generalized anti-Hamiltionan matrices under linear constraint is discussed. The necessary and sufficient conditions for constraint matrices set SA ≠φis provd, and the expression of the element of SA is given. For any n-by-n complex matrix A, It's optimal approximation matrix A is obtained.