Appendix: UnderstandingHyperdimensional ComputingforParallelSingle-PassLearning

Let(G,)be a finite group, and letX denote the set of its non-trivial irreducible characters. Any finite group VSA can be constructedinthisway. Alsoobservethat M hasrankgreaterthan 2. Now, suppose that there existed some representation ofM using vectors with entries in the unit circle inC. For this to hold, it would need to be the case thatM is in the convex combination of the similarity matrices generated by those entries, each of which must be of rank2. But, this is impossible, since (1) none of those matrices can be equal toM, and as such (2) any such matrix MC willhavetr(MCA)