No. An original Matrix, or just Trix for short, is basically any Matrix that is pre-Dye.
Before Dye bought the rights to the marker, which resulted in the '03 Dye LED and LCD models the Matrix was distributed first by a company called Generation E (commonly called Gen-E) and later, for a short time, by Diablo. All pre-Dye Trixes are generally lumped in to the Gen-E category.
Dye's Matrix lineage started with the '03 LED and LCD which looked basically the same as the original Matrix, only with slightly more metal milled off. In '04 they started the DM line with the DM4, or Dye Matrix 4, every successive year they have released a DM marker. In '05 Dye's sister brand Proto released the Proto Matrix, what we now know as the PM5 etc. Proto Trixes are usually comparable to the DM model from the prior year in terms of features etc.
An original Matrix is pretty much known for two things. First, they're big and rather blocky, leading to some using the knick name "fat body" Trix to describe them. Second, they are blazing fast.
In terms of paintball at large the Matrix line were the first of the spool valve markers to hit the market. They were, and still are, fast, quiet, have little kick and were easy on paint. Updated versions have addressed most of the marker's issues, especially efficiency, which on older Trixes is just this side of terrible without a decent set of after market internals and a bit of knowledge from the user on how to keep the gun properly tuned.
Hope that helps.
Could we spell it correctly...please?
Take a look, you might be surprised.