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Guiding MapReduce-based matrix multiplications with Quadtree Segmentation

I’ve been following the Linear Algebra series of lectures from MIT’s OpenCourseWare site. While watching Lecture 3 (I’m at Lecture 6 now), Professor Strang enumerates 5 methods of matrix multiplication. Two of those provided insights I wish my school teachers had provided me, but it was the fifth method which got me thinking.
The method is really a meta-method, and is a way of breaking down multiplication of large matrices in a recursive fashion. To demonstrate the idea, here’s a simple multiplication between two 2×2 matrices.
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