关于可对称化矩阵的Weyl-Лидский型定理

WEYL-ЛИДСКИЙ FORM THEORY FOR SYMMETRIZABLE MATRICES

建立了可对称化矩阵情形下的型定理和与近似不变子空间相关的特征值扰动分析.拓广了W Kahan的相应结果.

Let A,B∈(?)^(n×n) and H∈(?)^(l×l)(1≤l≤n-1) be symmetrizable matrices with eigenvalues α_1≥α_2≥…≥α_n, β_1≥β_2≥…≥β_n, μ_1≥μ_2≥…≥μ_n, i.e., there are nonsigular matrices P, Q, and S,such that P^(-1)AP=A_1, Q^(-1)BQ=B_1, S^(-1)HS=H_1, where A_1, B_1, H_1 are Hermitian matrices. Let R=AQ_1-Q_1H, Q_1∈(?)^(n×1) with singular values σ_1≥σ_2≥…≥σ_l>0, such that where α′_1, α′_2,…,α′_l ∈λ(A)={α_i}_(i-1)~n.