The sparse matrix multiplication algorithm can be seen here:
http://mathforum.org/library/drmath/view/51903.html
and at stackoverflow site too
http://stackoverflow.com/questions/15693584/fast-sparse-matrix-multiplication
The key to the linear algorithm is to find all non-zero entries in one the sparse matrix and then loop through them, update the impacted entries in the final result matrix.
Here is the code:
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