Processing large data in Mathematica

I'm dealing with large input arrays with Mathematica and it looks like I can't process anything bigger than (or equal to) 1024*1024 and 81*81*8开发者_开发技巧1. Is that normal? Should I be able to do computations on such input data? If so, how?

I think that depends on what calculations you are performing.

For example, in a very modest laptop:

Clear["Global`*"];
k = 2000;
Timing[a = Table[i j + i - j, {i, k}, {j, k}];
 MatrixPlot@a]  

Takes 20 seconds.

Matrix multiplying up to 1000x1000:

f[n_] := Table[RandomInteger[{1, n}], {n}, {n}];
ListLinePlot[
 Table[{n, First@AbsoluteTiming@(#.#) &@f[n]}, {n, 100, 1000, 100}]]  

So, it depends heavily on what you are trying to calculate.