The geometry of matrices

Abstract

In §§ 1-3 the matrix notation and theory of the stratified locus F | are developed, and two reflexive processes are defined. §§ 4-6 deal with rank and duality. In §§ 7-9 a matrix pencil is interpreted by means of Grace’s collineation defined by four [ k — 1]'s in in [2 k — 1] In § 10 constructions are given. §§ 11-13 interpret a non-singular matrix pencil in terms of reflexive operations; § 14 in terms of certain polar operations and nests of spaces. In § 15 these lead to rational normal loci and their osculating systems. §§ 16-19 interpret the minimal indices of a singular pencil in terms of reflexive processes. The minimal vectors are discussed in § 20, and latent loci in § 21, while § 22 reports shortly on the associated invariant theory.