LU Decomposition
Overview
The LU decomposition decomposes a matrix into the multiplication of a lower triangular matrix and an
upper triangular matrix.
A triangular matrix is one for which all values either above or below the diagonal are zero. For example,
the following is an upper triangular matrix.
{%
\begin{bmatrix}
a & b & c \\
0 & d & e\\
0 & 0 & f \\
\end{bmatrix}
%}
whereas a lower triangular matrix has the form
{%
\begin{bmatrix}
a & 0 & 0 \\
b & c & 0\\
d & e & f \\
\end{bmatrix}
%}
An LU decomposition, therefore, factors a given matrix A, into the product of two matrices as follows:
{% A = LU %}
Algorithm
The LU decomposition uses
Gaussian Elimination
Linear Algebra Module
let la = await import("/lib/linear-algebra/v1.0.0/linear-algebra.mjs");
let ans = la.LU(matrix1);
Try it!
