Problem in analyzing the program of Gauss Jordan Inverse problem

I had to code a program which calculates Inverse of a matrix by Gauss-Jordan Inverse method , I was trying to analyse the program and then code it myself.

http://hullooo.blogspot.in/2011/02/matrix-inversion-by-gauss-jordan.html

I understand it all except two things -

1) I don't understand how it does the row transformations.

2) While doing the Jordan method why the $j$ loop starts over and ends till last implying we are always pivoting that is moving the largest element up and hence I am unable to see a stable way of doing the left side part of the Augmented matrix to be an Identity matrix.

For reference to Jordan method I am using this link -

https://www.mathsisfun.com/algebra/matrix-inverse-row-operations-gauss-jordan.html

Any help is great! Am I leaving something or interpreting in a wrong way?

• I don't know what was the actual logic in the program in the above link but after little bit of googling I found another link where I got how it implements the row opertions and turning the left block of the Augmented matrix to an identity matrix. Here is the link - programming-techniques.com/2011/09/… Mar 22, 2017 at 5:36
• Do you really need the matrix inverse, or are you trying to solve a system of equations? In the latter case, you should look into the LU decomposition, which is essentially just Gaussian elimination, but it stores a reusable factorization of your matrix which can be used to repeatedly solve linear systems with the same left-hand side but different right-hand-sides. In addition, the LU decomposition is typically done in-place, making it consume far less memory than the augmented matrix method you're using. This obviously isn't an issue for small matrices, but presumably you want this to scale. Mar 23, 2017 at 17:27
• Nice, but $[A | I] \rightarrow [I|A^{-1}]$ is what I want to do,to convert $A$ to the Identity matrix i need to apply row operations but I donot understand the logic of looping things up to make that row operations work. Mar 24, 2017 at 1:21