Multiplying a matrix by its transpose

Multiplying a matrix by its transpose

An earlier post claimed that there practical advantages to partitioning a matrix, thinking of the matrix as a matrix of matrices. This post will give an example. Let M be a square matrix and suppose we need to multiply M by its transpose MT. We can compute this product faster than multiplying two arbitrary matrices of the same size by exploiting the fact that MMT will be a symmetric matrix. We start by partitioning M into four blocks Then and No…