For standard eigenvalue problems, a closed-form expression for the condition
numbers of a multiple eigenvalue is known. In particular, they are uniformly 1
in the Hermitian case, and generally take different values in the non-Hermitian
case. We consider the generalized eigenvalue problem and identify the condition
numbers of a multiple eigenvalue. Our main result is that a multiple eigenvalue
generally has multiple condition numbers, even in the Hermitian definite case.
The condition numbers are characterized in terms of the singular values of the
outer product of the corresponding left and right eigenvectors
