This paper concerns the Rayleigh–Ritz method for computing an approximation to an eigenspace X of a general matrix A from a subspace W that contains an approximation to X . The method produces a pair (N, X̃) that purports to approximate a pair (L,X), where X is a basis for X and AX = XL. In this paper we consider the convergence of (N, X̃) as the sine of the angle between X andW approaches zero. ...

1. Introduction. Let A be a topological space, F be a metrizable space, and C be the collection of continuous functions on X into Y. We shall be interested in two topologies on C. The compact-open or k-topology. Given compact subset K of X and open subset W of F, denote by (K, W) the collection of functions fEC such that fiK)E W. The assembly of finite intersections of sets iK, W) forms a base ...