Akihiro SUGIMOTO
Projection Invariants of (n-2)-Dimensional
Subspaces in n-Dimensional Projective Space
Abstract:When we observe a subject under investigation, we often obtain only a certain part of the original information, that is, information projected, from a space where the original information exists, to its subspace. We are then required to deal with such partial information to investigate the subject. When original information is subject to a given class of admissible transformations, projection invariants, functions in terms of the projected information whose values are unaffected by the class of admissible transformations, provide an essential relationship between the original information and the projected one. This paper presents a study on projection invariants under the conditions that the n-dimensional projective space is projected into the (n-1)-dimensional space and the class of admissible transformations involves projective transformations. We show the existence of a projection invariant derived from (n+i+j) linear subspaces of dimension (n-2) arranged in the letter H, where i and j are given integers such that 1 ≦ i ≦ j ≦ n-i. The nonsingularity condition, i.e., the condition under which the projection invariant is nonsingular, is also given.
Key Words: projection invariants, admissible transformations, interpretation vector, intersections of hyperplanes, nonsingularity condition.