Admittedly, I could have figured it out through trial and error, but I would also like to know whether or not this number varies and how (computer performance, other data structures present, compiler type, etc.). Thanks!
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You will need to increase you JVM heap size if you run out of memory, read this. Nothing you can do if your matrix requires a lot of memory (if there is no memory leaks) other than increasing the heap size.
You can change the size of your matrix as large as you want (but not bigger than the maximum value of integer which is used as index) if you have enough memory. Integer is 32bits so, you have the maximum theoretical limit there.