I got my first computer a couple of years after The Matrix came out.  It's one of my all  time favorites and I wanted a username that tied in to the movie somehow.
Seems like all my choices were already taken.  My first choice was "Agent Smith", lol.  Thanks alot Kirk.  ;P
Then one day I was looking through some game hacks (cheat codes) and came across one called "Matrix Mode".  Sounded good to me at the time.  I first used it on Xbox LIve.  The name sort of grew on me and now I've been using it so long it's difficult to change.
I have it in lowercase letters 'cause to me it's more a state of mind than a name.  :)

"Simplicity is the ultimate sophistication." Leonardo da Vinci