在结构的振动和稳定性分析中经常遇到下列形式的广义特征值问题:求特征值λ和相应的特征向量x,使 (K-λM)x=0 (1)或 (Mλ~2-Cλ-K)x=0 (2)或 (Mλ~2+Cλ+K)x=0 (3)其中M,C是对称矩阵,C是反对称矩阵,M还是正定的,假定在(2)和(3)中的K是对称正定的,而(1)中的K可以是对称的,也可以是反对称的,甚至,更一般地,可以是规范的(即满足 The following generalized eigenvalue problems are often encountered in the structural vibration and stability analysis: Find the eigenvalue λ and the corresponding eigenvector x such that (K-λM) x = 0 (1) or (Mλ ~ 2-Cλ (3) where M and C are symmetric matrices, C is an antisymmetric matrix, and M is still positive definite, assuming that in (2) and (3), K is symmetrically positive definite, and K in (1) can be symmetrical or antisymmetric, and even more generally it can be canonical