正则矩阵对的广义特征值扰动定理

ON PERTURBATION THEOREMS FOR THE GENERALIZED EIGENVALUES OF REGULAR MATRIX PAIRS

1.引言 关于普通特征值扰动的Bauer-Fike定理已被推广到A为非可对角化的情形.与此相应,广义特征值的扰动问题,亦有类似的结论.将[1]中的结论稍加改进并且推广至一般正则对的情形,是本文一部分内容,另一部分是研究广义近似特征值以及广义近似不变子空间的特征值扰动,本文采用的范数不局限于谱范数,而是一般的p-范数(1≤p≤+∞).

In this paper, we study the Bauer-Fike type theorem for regular matrix pairs, and on thebasis of the W-J canonical form, its general form is given. Besides, we also obtain some bo-unds for measuring an approximate generalized eigenvalue and for the perturbation of genera-lized eigenvalues of an approximate generalized invariant subspace. To estimate all these bo-unds, the p-norm and a 'metric' called 'p-chordal metric' which is not a metric when p?2are used.