Equivalence of projections as gauge equivalence on noncommutative space

Projections play crucial roles in the ADHM construction on noncommutative R -4. In this article a framework for the description of equivalence relation s between projections is proposed. We treat the equivalence of projections as gauge equivalence" on noncommutative space. We find an interesting appli cation of this framework to the study of the U(2) instanton on noncommutati ve R-4: A zero winding number configuration with a hole at the origin is "g auge equivalent" to the noncommutative analog of the BPST instanton. Thus t he "gauge transformation" in this case can be understood as a noncommutativ e resolution of the singular gauge transformation in ordinary R-4.