Matrix Inverse
Overview
The matrix inverse of a matrix {% A %}, {% A^{-1} %} is the matrix such
{% A^{-1}A = I %}
and
{% AA^{-1} = I %}
if such a matrix exists.
Matrix Inverse Algorithm
The algorithm for computing the matrix inverse is based on the
LU decomposition.
First, it computes the LU decomposition of the matrix
{% M = LU %}
Then, it computes the inverse of the L and U matrices.
{% (LU)^{-1} = U^{-1} L^{-1} %}
When partial pivoting is used in the LU decomposition, the pivoting must be undone.
Computing Matrix Inverse
The linear-algebra module provides a method for calculating the matrix inverse.
let la = await import('/lib/liniear-albgebra/v1.0.0/linear-algebra.mjs');
var ans = la.inverse(matrix1);
Try it!
