We analyze necessary and sufficient conditions on a nonsingular matrix A such that, for any initial vector r₀, an orthogonal basis of the Krylov subspaces ${\cal K}_{n}(A,r_{0})$ is generated by a ...

The problem of calculating the eigensystem of a general complex matrix is well known. In many cases, however, the eigensystem is poorly determined numerically in the sense that small changes in the ...