The nonunique shorted matrix

Abstract

Goller (1986) gave an explicit expression for a shorted matrix as defined by Mitra and Puri (1982) and Mitra (1982) in situations where the shorted matrix is not unique. In this paper, the authors provide an alternative approach to the same problem which may give deeper insight into it. In this development, certain concepts such as quasiidempotent matrices and the separability of subspaces of row and column spans of a matrix with reference to the same matrix play an interesting role, as shown by Mitra. Under certain regularity conditions the shorted matrix has some interesting properties similar to the ones noted by Anderson and Trapp for their unique shorted operator. A detailed investigation is made of how many of these properties are realized in the nonunique case.