### Symmetric Matrices

A symmetric matrix looks like this:

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

Continue reading Matrix Theory: Linear transformations and Basis vectors

A symmetric matrix looks like this:

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

Continue reading Matrix Theory: Linear transformations and Basis vectors

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.

Continue reading Guiding MapReduce-based matrix multiplications with Quadtree Segmentation