Loading [MathJax]/extensions/TeX/boldsymbol.js

 

 

 

LU Decomposition, the inverse of a matrix

If the inverse exists then \mathbf{A}^{-1}\mathbf{A}=\mathbf{I}, the identity matrix. With an LU decomposed matrix we can rewrite the last equation as \mathbf{LU}\mathbf{A}^{-1}=\mathbf{I}.