中文摘要：

讨论H矩阵的性质，给出H-对称矩阵和H-反对称矩阵的结构，证明若x是H-对称矩阵或H-反对称矩阵A-λB的特征向量，则工是H-对称向量或H-反对称向量，或者x可以由H-对称向量及H-反对称向量线性表示，并根据A-λB的特征向量的上述特点，得到H-对称矩阵和H-反对称矩阵的广义特征值反问题AX=BXA解的表达式．

英文摘要：

Properties of H-matrices were discussed, the structures of H-symmetric and H-antisymmetric matrices were given, and it was proven that when x was an eigenvector of H-symmetric matrices or H-anti- symmetric matrices A-λB, x would be either an H-symmetric vector, or H-antisymmetric vector, or x could be expressed by linear combination of H-symmetric vector with H-antisymmetric vector. Based on a- bove-mentioned feature of eigenvector of A-λB, the expression of solution to inverse problem AX=BXA of generalized eigenvalue of H-symmetric matrices and H-antisymmetric matrices were obtained.