(untitled) (Journal of Computational Mathematics, 1998)
In this paper, the unitarily invariant norm \|·\| on C^m× n is used. We first discuss the problem under what case, a rectangular matrix A has minimum condition number K (A)=\| A \| \|A^+\|, where A^+ designates the Moore-Penrose inverse of A; and under what condition, a square matrix A has minimum condition number for its eigenproblem? Then we consider the second problem, i.e., optimum of K (A)=\|A\| \|A^-1\|_2 in error estimation.