ABSTRACT
This chapter discusses a structure a “path invariant matrix system.” Points in some space are linked by edges that are labeled with matrices in such a way that the matrix product taken along any path depends only on the endpoints. The path invariance condition on minimal loops induces polynomial equations among the matrix elements. A successful solution then provides a limitless space of closed contours, each yielding a correct identity, several of which may be concise enough to be interesting. The grids for most of the standard series transformations are just “railroad tracks”. Telescopy takes place between a single rail and a black hole. The problem is to find columnar, “diving in” matrices which path-invariantly connect the black hole to all the nodes along the rail. Then the telescoping identity is the equivalence between diving straight in, and performing the sum prior to diving in.
