Locating a nearest matrix with an eigenvalue of prespecified algebraic multiplicity (Q537877)

The author proposes an extension of the Wilkinson distance in matrices which is defined as the two-norm of the smallest perturbation that makes the matrix have multiple eigenvalues. In this approach, the \(r\)-version of this distance is defined such that the perturbed matrix has an eigenvalue of multiplicity of \(r\) or higher. He begins with the background section on previous work on this topic, followed by a section where the single value characterization of the extended distance is provided with proof. The third section moves onto the computation of the Wilkinson distance itself, followed by a section presenting a summary of the numerical experimentation and a discussion on its computational efficiency.