On worst-case condition numbers of a nondefective multiple eigenvalue

Summary.

This paper is a continuation of the author [6] in Numerische Mathematik. Let $\lambda_1$ be a nondefective multiple eigenvalue of multiplicity$r$ of an $n \times n$ complex matrix $A$, and let$c_1(A; \lambda_1) \geq \cdots \geq c_r(A; \lambda_1)$ be the secants of the canonical angles between the left and right invariant subspaces of $A$ corresponding to the multiple eigenvalue $\lambda_1$. The analysis of this paper shows that the quantities$\hat{c}_j(A; \lambda_1) \equiv \left( \prod_{k=1}^{j}c_k(A; \lambda_1) \right)^{1/j},\;\;\;\;j=1, \ldots, r$ are the worst-case condition numbers of the multiple eigenvalue$\lambda_1$ .