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