论文信息 - Properties of a matrix with a very ill-conditioned eigenproblem

Properties of a matrix with a very ill-conditioned eigenproblem

It is proved that a matrix that has a very ill-conditioned eigenvector matrix is close to one that has multiple eigenvalues, and an estimate of this distance is given, measured in the Euclidean matrix norm.

Axel Ruhe

[1] P. Henrici. Bounds for iterates, inverses, spectral variation and fields of values of non-normal matrices , 1962 .

[2] Alston S. Householder,et al. The Theory of Matrices in Numerical Analysis , 1964 .

[3] J. H. Wilkinson. The algebraic eigenvalue problem , 1966 .

[4] J. Varah,et al. Computing Invariant Subspaces of a General Matrix when the Eigensystem is Poorly Conditioned , 1970 .