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)\](http://s.wordpress.com/latex.php?latex=%20%20A%3D%20%20%5Cleft%28%20%5Cbegin%7Barray%7D%7Bcccc%7D%20%20a%20%26%20d%20%26%20n%20%26%20w%20%5C%5C%20%20d%20%26%20b%20%26%20h%20%26%20e%20%5C%5C%20%20n%20%26%20h%20%26%20c%20%26%20i%20%5C%5C%20%20w%20%26%20e%20%26%20i%20%26%20d%20%5Cend%7Barray%7D%20%5Cright%29%5C%20%20&bg=ffffff&fg=000000&s=0 "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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Tagged: math
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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