Numerical Analysis

Here are notes written when I was taking the numerical lienar algebra course (CME 302, Stanford). In these notes, we explain the observation that how those seemly miraculous matrix decompositions can be derived from the general theory of Lie algebras.  In the correspondence between the LU decomposition and Bruhat decomposition, there is a mild difference between them.

For smilar results, see : [1307.5132] Every matrix is a product of Toeplitz matrices (arxiv.org) .