GaussElimination[X]

Aliases: GauE

Description: $GaussElimination[X]$ is the formula for 2$\times$2 block gauss elimination of $X$. It returns 3 block 2$\times$2 matrices which are the block $L D U$ decomposition of $X$.

Arguments: $X$ is a block 2$\times$2 matrix.

Comments / Limitations: If $X$ is the block 2$\times$2 matrix of the form $\{\{a,b\},\{c,d\}\}$, then we assume that $a$ is invertible. If you want to assume that $d$ is invertible, type $GaussElimination[X, btm]$. $GaussElimination[X]$ is the same as $GaussElimination[X, top]$. Note the Schur complement for $X$ can be extracted from the diagonal matrix $D$, so we did not make it a separate function.