# Matrix Theory: Linear transformations and Basis vectors

### Symmetric Matrices

A symmetric matrix looks like this:

$A= \left( \begin{array}{cccc} a & d & n & w \\ d & b & h & e \\ n & h & c & i \\ w & e & i & d \end{array} \right)\$

Notice how the values are reflected across the diagonal a-b-c-d; this holds true for any symmetric matrix.
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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.