You may want to have a look at:
SD card storage and really easy to use. Connects to a serial port (software serial port will work too).
See here for Arduino libraries:
http://www.roguerobotics.com/wikidocs/code/library/arduino/roguesd
You could save your matrices on shutdown, and load them back up on restart.
Heck, I'd even help you write the code to save a load the data. Piece of cake.
b