On the condition numbers of a multiple eigenvalue of a generalized eigenvalue problem (Q443858)

The author deals with the condition numbers of a multiple eigenvalue of a generalized eigenvalue problem. First under Hermitian perturbations of a Hermitian definite pair with a nondefective multiple finite eigenvalue, the author provides the condition numbers of this eigenvalue. After, he provides the condition numbers of a finite multiple eigenvalue of a non Hermitian pair under non Hermitian perturbations. These condition numbers are characterized in terms of the singular values of the outer product of the corresponding left and right eigenvectors. In addition, the author also studies the case of an infinite and/or defective eigenvalue. Numerical examples are also given to illustrate the results of the article.