LU Decomposition

A method for Matrix Factorization and solving $Ax=b$ for $x$

$$\begin{array}{r}Ax=b=LUx\end{array}$$

We then set $Ux=y$, giving us $Ly=b$. Since $L$ is lower triangular, and U is upper triangular, we an easily solve the two linear systems by substitution.

Using the matrix inverse is inefficient and numerically unstable.

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