I was wondering how can matlab multiply two matrices so fast. When multiplying two NxN matrices, N^3 multiplications are performed. Even with the Strassen Algorithm it takes N^2.8 multiplications, which is still a large number. I was running the following test program:

a = rand(2160); b = rand(2160); tic;a*b;toc 

2160 was used because 2160^3=~10^10 ( a*b should be about 10^10 multiplications)

I got:

Elapsed time is 1.164289 seconds. 

(I'm running on 2.4Ghz notebook and no threading occurs) which mean my computer made ~10^10 operation in a little more than 1 second.

How this could be??