# 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/… – BAYMAX Mar 22 '17 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. – Tyler Olsen Mar 23 '17 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. – BAYMAX Mar 24 '17 at 1:21